ECE 204 Numerical Methods for Computer Engineers MIDTERM EXAMINATION /4:30-6:00
|
|
- Frederick Owen
- 5 years ago
- Views:
Transcription
1 ECE 4 Numerical Methods for Computer Engineers ECE 4 Numerical Methods for Computer Engineers MIDTERM EXAMINATION --7/4:-6: The eamination is out of marks. Instructions: No aides. Write your name and student ID number on each booklet. Turn off all electronic media and store them under your desk. Write all your answers in your booklets. Answer the questions order in which they appear on the eamination. If you need to write your answer to a question elsewhere as a result of space considerations, please indicate this. You may ask only two questions during the eamination:. May I go to the washroom?. May I have another booklet? At the end of the eam, place the eam paper and any additional booklets into the first booklet. Do not leave during the first minutes of the eamination. Do not leave during the last minutes of the eamination. Do not stand up until all eams have been picked up. Attention: The questions are in the order of the course material, not in order of difficulty. I have read and understood all of these instructions: Name: Signature: Page of 4
2 ECE 4 Numerical Methods for Computer Engineers Error Analysis and Numeric Representation. [] Multiply the two binary numbers. and.. Round your answer to bits.. [] Using decimal digits of precision for each arithmetic operations, evaluate the two equivalent epressions ( ) and for =.9. Which is more accurate?. [] What number does the headecimal double-precision floating-point number c 98 represent? 4. [] Using four decimal digits of precision, given a =., b =.4, and c =.4, show that (a + b) + c? a + (b + c). Linear Algebra. [6] Find the three matrices P T, L, and U of the LUP-decomposition of the matri [4] Find the Cholesky decomposition of the matri [] Show that if A is invertible, that is Av = if and only if v =, then A T A is positive definite. You may need one or more of: (A T B T ) = (BA) T T A > Av = A v v = v T v Page of 4
3 ECE 4 Numerical Methods for Computer Engineers 8. [] Suppose that you wanted to calculate the maimum eigenvalue of M T M for a given matri M. Using asymptotic analysis (big-o), which of the following two functions would you use, and why? function lambda = eigen( M ) v = rand( length( M ), ); for i=: v = (M *M)*v/norm(v); end; lambda = norm( v ); end function lambda = eigen( M ) v = rand( length( M ), ); for i=: v = M *(M*v)/norm(v); end; lambda = norm( v ); end 9. [] Perform three iterations of the algorithm for finding the maimum eigenvalue of a 4 matri M = starting with the vector v =. Will this iteration process 4 converge?. [] Given the vector v = (,,, ) T, which has v =, use the appropriate matri norm to find the maimum possible value of Mv when 4 M = 7 4 Given that Mv = 8, find the relative error of your approimation.. [] Perform one iteration of the Jacobi method and one iteration of the Gauss-Seidel method to solve the system of linear equations given by = starting with the vector = (,, ) T. Interpolation. [] Write down the Vandermonde matri which must be solved to find the quadratic polynomial interpolating the points (-, ), (, 4), (, 7). Page of 4
4 ECE 4 Numerical Methods for Computer Engineers. [] Write down the Lagrange polynomial which interpolates the three points (-, ), (, ), (4, ). 4. [] Use the table of divided differences 4 6 to help you find the Newton polynomial which interpolates the four points (, ), (4, ), (, 6), and (6, ).. [] Use Horner s rule to evaluate at = 4 the Newton polynomial defined by the coefficient vector (-, -, ) corresponding to the values (,, ). Least Squares Regression 6. [] Write down the generalized Vandermonde matri used to find the best-fitting straight line which passes through the five points (-, ), (, 4), (, ), (7, ), (9, ). 7. [] Given n points (, y ),..., ( n, y n ), assume that the column vector of -values is assigned to the variable and the column vector of y-values is assigned to the variable y. Write down the Matlab code necessary to find a solution vector c which represents the best-fitting quadratic polynomial and evaluate that solution vector at the point =.. 8. [] Find the best-fitting line passing through the origin of the five points (, 6.), (, 8), (, 7), (, 8.), (, ). Matlab 9. [] Recalling that the Matlab function ma optionally returns two values, e.g., >> [m, posn] = ma( [ - -] ) m = posn = 6 Given an n n matri M, assign to the variable s that entry in the matri which is in the column which has the ma imum column sum and which is in the row which has the minimum row sum.. [] What is the result of the Matlab command >> v = :. :.7 Page 4 of 4
5 ECE 4 Numerical Methods for Computer Engineers Page of and -.8. The first is more accurate and ,...., T A T A = (A) T (A) = A >. 8. Answer: the second, as M *(M*v) is two O(n ) operation while (M *M)*v is an O(n ) and an O(n ) operation. 9. (4, ) T, (, ) T, (4, ) T. The sequence does not converge.. = 6, relative error is... and.... V = 4. 4) ( 4) )( ( ) ( 4) ( ( ) + ( )( 4) + ( )( 4)( ). s = s = s(4 ) = -
6 ECE 4 Numerical Methods for Computer Engineers s = s(4 ) = - 6. V = V = vander( ) or V = [.^ ones( n, )] V \ y or (V * V) \ (V * y) 8. y =. 9. [m, cl] = ma( sum( M ) ); [m, rw] = min( sum( M ) ); s = M(rw, cl). (,.,,.) Page 6 of 4
Assignment 2. with (a) (10 pts) naive Gauss elimination, (b) (10 pts) Gauss with partial pivoting
Assignment (Be sure to observe the rules about handing in homework). Solve: with (a) ( pts) naive Gauss elimination, (b) ( pts) Gauss with partial pivoting *You need to show all of the steps manually.
More informationCS 6210 Fall 2016 Bei Wang. Review Lecture What have we learnt in Scientific Computing?
CS 6210 Fall 2016 Bei Wang Review Lecture What have we learnt in Scientific Computing? Let s recall the scientific computing pipeline observed phenomenon mathematical model discretization solution algorithm
More informationCollege Algebra Final Exam Review. 5.) State the domain of the following functions. Then determine whether each function is a one-toone function.
College Algebra Final Eam Review For # use the given graph f():.) Find f( )..) State the zeros, the domain, and the range. f().) State the local maimum and/or minimum..) State the intervals decreasing
More informationParallel Implementations of Gaussian Elimination
s of Western Michigan University vasilije.perovic@wmich.edu January 27, 2012 CS 6260: in Parallel Linear systems of equations General form of a linear system of equations is given by a 11 x 1 + + a 1n
More informationLinear Equation Systems Iterative Methods
Linear Equation Systems Iterative Methods Content Iterative Methods Jacobi Iterative Method Gauss Seidel Iterative Method Iterative Methods Iterative methods are those that produce a sequence of successive
More informationNUMERICAL METHODS, NM (4776) AS
NUMERICAL METHODS, NM (4776) AS Objectives To provide students with an understanding that many mathematical problems cannot be solved analytically but require numerical methods. To develop a repertoire
More informationMIDTERM EXAMINATION Douglas Wilhelm Harder EIT 4018 x T09:30:00P1H20M Rooms: RCH-103 and RCH-302
ECE 250 Algorithms and Data Structures MIDTERM EXAMINATION Douglas Wilhelm Harder dwharder@uwaterloo.ca EIT 4018 x37023 2013-10-23T09:30:00P1H20M Rooms: RCH-103 and RCH-302 Instructions: Read and initial
More informationContents. I The Basic Framework for Stationary Problems 1
page v Preface xiii I The Basic Framework for Stationary Problems 1 1 Some model PDEs 3 1.1 Laplace s equation; elliptic BVPs... 3 1.1.1 Physical experiments modeled by Laplace s equation... 5 1.2 Other
More informationSECOND SEMESTER BCA : Syllabus Copy
BCA203T: DATA STRUCTURES SECOND SEMESTER BCA : Syllabus Copy Unit-I Introduction and Overview: Definition, Elementary data organization, Data Structures, data structures operations, Abstract data types,
More informationChapter 3. Interpolation. 3.1 Introduction
Chapter 3 Interpolation 3 Introduction One of the fundamental problems in Numerical Methods is the problem of interpolation, that is given a set of data points ( k, k ) for k =,, n, how do we find a function
More informationCumulative Review Problems Packet # 1
April 15, 009 Cumulative Review Problems Packet #1 page 1 Cumulative Review Problems Packet # 1 This set of review problems will help you prepare for the cumulative test on Friday, April 17. The test will
More informationES 240: Scientific and Engineering Computation. a function f(x) that can be written as a finite series of power functions like
Polynomial Deinition a unction () that can be written as a inite series o power unctions like n is a polynomial o order n n ( ) = A polynomial is represented by coeicient vector rom highest power. p=[3-5
More informationMCS 118 Quiz 1. Fall (5pts) Solve the following equations for x. 7x 2 = 4x x 2 5x = 2
MCS 8 Quiz Fall 6. (5pts) Solve the following equations for. 7 = 4 + 3. (5pts) Solve the following equations for. 3 5 = 3. (5pts) Factor 3 + 35 as much as possible. 4. (5pts) Simplify +. 5. (5pts) Solve
More information3. Replace any row by the sum of that row and a constant multiple of any other row.
Math Section. Section.: Solving Systems of Linear Equations Using Matrices As you may recall from College Algebra or Section., you can solve a system of linear equations in two variables easily by applying
More informationFebruary 23 Math 2335 sec 51 Spring 2016
February 23 Math 2335 sec 51 Spring 2016 Section 4.1: Polynomial Interpolation Interpolation is the process of finding a curve or evaluating a function whose curve passes through a known set of points.
More informationAMSC/CMSC 460 Final Exam, Fall 2007
AMSC/CMSC 460 Final Exam, Fall 2007 Show all work. You may leave arithmetic expressions in any form that a calculator could evaluate. By putting your name on this paper, you agree to abide by the university
More informationFinite Math - J-term Homework. Section Inverse of a Square Matrix
Section.5-77, 78, 79, 80 Finite Math - J-term 017 Lecture Notes - 1/19/017 Homework Section.6-9, 1, 1, 15, 17, 18, 1, 6, 9, 3, 37, 39, 1,, 5, 6, 55 Section 5.1-9, 11, 1, 13, 1, 17, 9, 30 Section.5 - Inverse
More informationCurriculum Map: Mathematics
Curriculum Map: Mathematics Course: Honors Advanced Precalculus and Trigonometry Grade(s): 11-12 Unit 1: Functions and Their Graphs This chapter will develop a more complete, thorough understanding of
More informationContents. I Basics 1. Copyright by SIAM. Unauthorized reproduction of this article is prohibited.
page v Preface xiii I Basics 1 1 Optimization Models 3 1.1 Introduction... 3 1.2 Optimization: An Informal Introduction... 4 1.3 Linear Equations... 7 1.4 Linear Optimization... 10 Exercises... 12 1.5
More informationUNIVERSITY OF CALIFORNIA COLLEGE OF ENGINEERING
UNIVERSITY OF CALIFORNIA COLLEGE OF ENGINEERING E7: INTRODUCTION TO COMPUTER PROGRAMMING FOR SCIENTISTS AND ENGINEERS Professor Raja Sengupta Spring 2010 Second Midterm Exam April 14, 2010 [30 points ~
More information1 2 (3 + x 3) x 2 = 1 3 (3 + x 1 2x 3 ) 1. 3 ( 1 x 2) (3 + x(0) 3 ) = 1 2 (3 + 0) = 3. 2 (3 + x(0) 1 2x (0) ( ) = 1 ( 1 x(0) 2 ) = 1 3 ) = 1 3
6 Iterative Solvers Lab Objective: Many real-world problems of the form Ax = b have tens of thousands of parameters Solving such systems with Gaussian elimination or matrix factorizations could require
More informationI. This material refers to mathematical methods designed for facilitating calculations in matrix
A FEW CONSIDERATIONS REGARDING MATRICES operations. I. This material refers to mathematical methods designed for facilitating calculations in matri In this case, we know the operations of multiplying two
More informationDM6 Support Vector Machines
DM6 Support Vector Machines Outline Large margin linear classifier Linear separable Nonlinear separable Creating nonlinear classifiers: kernel trick Discussion on SVM Conclusion SVM: LARGE MARGIN LINEAR
More information8/27/2016. ECE 120: Introduction to Computing. Graphical Illustration of Modular Arithmetic. Representations Must be Unambiguous
University of Illinois at Urbana-Champaign Dept. of Electrical and Computer Engineering ECE 120: Introduction to Computing Signed Integers and 2 s Complement Strategy: Use Common Hardware for Two Representations
More information(Creating Arrays & Matrices) Applied Linear Algebra in Geoscience Using MATLAB
Applied Linear Algebra in Geoscience Using MATLAB (Creating Arrays & Matrices) Contents Getting Started Creating Arrays Mathematical Operations with Arrays Using Script Files and Managing Data Two-Dimensional
More informationInterpolation. TANA09 Lecture 7. Error analysis for linear interpolation. Linear Interpolation. Suppose we have a table x x 1 x 2...
TANA9 Lecture 7 Interpolation Suppose we have a table x x x... x n+ Interpolation Introduction. Polynomials. Error estimates. Runge s phenomena. Application - Equation solving. Spline functions and interpolation.
More informationNonlinear Programming
Nonlinear Programming SECOND EDITION Dimitri P. Bertsekas Massachusetts Institute of Technology WWW site for book Information and Orders http://world.std.com/~athenasc/index.html Athena Scientific, Belmont,
More informationMathematics 4330/5344 #1 Matlab and Numerical Approximation
David S. Gilliam Department of Mathematics Texas Tech University Lubbock, TX 79409 806 742-2566 gilliam@texas.math.ttu.edu http://texas.math.ttu.edu/~gilliam Mathematics 4330/5344 #1 Matlab and Numerical
More informationNatural Numbers and Integers. Big Ideas in Numerical Methods. Overflow. Real Numbers 29/07/2011. Taking some ideas from NM course a little further
Natural Numbers and Integers Big Ideas in Numerical Methods MEI Conference 2011 Natural numbers can be in the range [0, 2 32 1]. These are known in computing as unsigned int. Numbers in the range [ (2
More informationToday is the last day to register for CU Succeed account AND claim your account. Tuesday is the last day to register for my class
Today is the last day to register for CU Succeed account AND claim your account. Tuesday is the last day to register for my class Back board says your name if you are on my roster. I need parent financial
More informationTime: 1 hour 30 minutes
Paper Reference(s) 666/0 Edecel GCE Core Mathematics C Bronze Level B Time: hour 0 minutes Materials required for eamination Mathematical Formulae (Green) Items included with question papers Nil Candidates
More informationECE 250 Data Structures and Algorithms MID-TERM EXAMINATION /08:30-9:50 RCH 105, RCH 110
ECE 250 Data Structures and Algorithms MID-TERM EXAMINATION 2009-10-29/08:30-9:50 RCH 105, RCH 110 Instructions: There are 70 marks and the examination will be marked out of 65. No aides. Turn off all
More information(Sparse) Linear Solvers
(Sparse) Linear Solvers Ax = B Why? Many geometry processing applications boil down to: solve one or more linear systems Parameterization Editing Reconstruction Fairing Morphing 2 Don t you just invert
More informationReals 1. Floating-point numbers and their properties. Pitfalls of numeric computation. Horner's method. Bisection. Newton's method.
Reals 1 13 Reals Floating-point numbers and their properties. Pitfalls of numeric computation. Horner's method. Bisection. Newton's method. 13.1 Floating-point numbers Real numbers, those declared to be
More informationObjectives and Homework List
MAC 1140 Objectives and Homework List Each objective covered in MAC1140 is listed below. Along with each objective is the homework list used with MyMathLab (MML) and a list to use with the text (if you
More informationAddition/Subtraction flops. ... k k + 1, n (n k)(n k) (n k)(n + 1 k) n 1 n, n (1)(1) (1)(2)
1 CHAPTER 10 101 The flop counts for LU decomposition can be determined in a similar fashion as was done for Gauss elimination The major difference is that the elimination is only implemented for the left-hand
More informationHandout 4 - Interpolation Examples
Handout 4 - Interpolation Examples Middle East Technical University Example 1: Obtaining the n th Degree Newton s Interpolating Polynomial Passing through (n+1) Data Points Obtain the 4 th degree Newton
More informationTHE DEVELOPMENT OF THE POTENTIAL AND ACADMIC PROGRAMMES OF WROCLAW UNIVERISTY OF TECH- NOLOGY ITERATIVE LINEAR SOLVERS
ITERATIVE LIEAR SOLVERS. Objectives The goals of the laboratory workshop are as follows: to learn basic properties of iterative methods for solving linear least squares problems, to study the properties
More informationWorking with Rational Expressions
Working with Rational Expressions Return to Table of Contents 4 Goals and Objectives Students will simplify rational expressions, as well as be able to add, subtract, multiply, and divide rational expressions.
More informationPRACTICE FINAL - MATH 1210, Spring 2012 CHAPTER 1
PRACTICE FINAL - MATH 2, Spring 22 The Final will have more material from Chapter 4 than other chapters. To study for chapters -3 you should review the old practice eams IN ADDITION TO what appears here.
More informationMidterm Exam with solutions
Midterm Exam with solutions CS227-Introduction to Scientific Computation November 8, 2011 1. The following is a transcript of a MATLAB session. >> x=1/62.5 x = 0.016000000000000 >> y=(1+x)-1 y = 0.016000000000000
More informationTest 2 - Python Edition
'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ EGR 13L Spring 218 Test 2 - Python Edition Shaundra B. Daily & Michael R. Gustafson II Name (please print): NetID (please print): In keeping with the Community
More informationSection Rational Functions and Inequalities. A rational function is a quotient of two polynomials. That is, is a rational function if
Section 6.1 --- Rational Functions and Inequalities A rational function is a quotient of two polynomials. That is, is a rational function if =, where and are polynomials and is not the zero polynomial.
More informationPrecalculus Notes Unit 1 Day 1
Precalculus Notes Unit Day Rules For Domain: When the domain is not specified, it consists of (all real numbers) for which the corresponding values in the range are also real numbers.. If is in the numerator
More informationSYSTEMS OF NONLINEAR EQUATIONS
SYSTEMS OF NONLINEAR EQUATIONS Widely used in the mathematical modeling of real world phenomena. We introduce some numerical methods for their solution. For better intuition, we examine systems of two
More informationNumerical Analysis I - Final Exam Matrikelnummer:
Dr. Behrens Center for Mathematical Sciences Technische Universität München Winter Term 2005/2006 Name: Numerical Analysis I - Final Exam Matrikelnummer: I agree to the publication of the results of this
More informationBACHELOR OF COMPUTER APPLICATIONS (BCA)
BACHELOR OF COMPUTER APPLICATIONS (BCA) BCA/ASSIGN/V/YEAR/2012 ASSIGNMENTS Year, 2012 (5 th Semester (Pre-Revised)) CS-68 CS-69 BCS-61 CS-70 CS-71 SCHOOL OF COMPUTER AND INFORMATION SCIENCES INDIRA GANDHI
More informationMA 323 Geometric Modelling Course Notes: Day 28 Data Fitting to Surfaces
MA 323 Geometric Modelling Course Notes: Day 28 Data Fitting to Surfaces David L. Finn Today, we want to exam interpolation and data fitting problems for surface patches. Our general method is the same,
More informationIntroduction to Rational Functions Group Activity 5 Business Project Week #8
MLC at Boise State 013 Defining a Rational Function Introduction to Rational Functions Group Activity 5 Business Project Week #8 f x A rational function is a function of the form, where f x and g x are
More informationIntroduction to Programming for Engineers Spring Final Examination. May 10, Questions, 170 minutes
Final Examination May 10, 2011 75 Questions, 170 minutes Notes: 1. Before you begin, please check that your exam has 28 pages (including this one). 2. Write your name and student ID number clearly on your
More informationCS 395T Lecture 12: Feature Matching and Bundle Adjustment. Qixing Huang October 10 st 2018
CS 395T Lecture 12: Feature Matching and Bundle Adjustment Qixing Huang October 10 st 2018 Lecture Overview Dense Feature Correspondences Bundle Adjustment in Structure-from-Motion Image Matching Algorithm
More informationMath 355: Linear Algebra: Midterm 1 Colin Carroll June 25, 2011
Rice University, Summer 20 Math 355: Linear Algebra: Midterm Colin Carroll June 25, 20 I have adhered to the Rice honor code in completing this test. Signature: Name: Date: Time: Please read the following
More informationX Std. Topic Content Expected Learning Outcomes Mode of Transaction
X Std COMMON SYLLABUS 2009 - MATHEMATICS I. Theory of Sets ii. Properties of operations on sets iii. De Morgan s lawsverification using example Venn diagram iv. Formula for n( AÈBÈ C) v. Functions To revise
More information(Sparse) Linear Solvers
(Sparse) Linear Solvers Ax = B Why? Many geometry processing applications boil down to: solve one or more linear systems Parameterization Editing Reconstruction Fairing Morphing 1 Don t you just invert
More informationNumerical Analysis Fall. Numerical Differentiation
Numerical Analysis 5 Fall Numerical Differentiation Differentiation The mathematical definition of a derivative begins with a difference approimation: and as is allowed to approach zero, the difference
More informationECE 250 Data Structures and Algorithms MIDTERM EXAMINATION /5:30-7:00
The examination is out of 66 marks. ECE 250 Data Structures and Algorithms MIDTERM EXAMINATION 2007-10-25/5:30-7:00 Instructions: No aides. Turn off all electronic media and store them under your desk.
More informationCS321 Introduction To Numerical Methods
CS3 Introduction To Numerical Methods Fuhua (Frank) Cheng Department of Computer Science University of Kentucky Lexington KY 456-46 - - Table of Contents Errors and Number Representations 3 Error Types
More informationFitting to a set of data. Lecture on fitting
Fitting to a set of data Lecture on fitting Linear regression Linear regression Residual is the amount difference between a real data point and a modeled data point Fitting a polynomial to data Could use
More informationSolving General Linear Equations w/ Excel
Solving General Linear Equations w/ Ecel Matri Operations in Ecel Ecel has commands for: Multiplication (mmult) matri multiplication Transpose (transpose) transpose a matri Determinant (mdeterm) calc the
More informationMaclaurin series. To create a simple version of this resource yourself using Geogebra:
Maclaurin series Maclaurin series (Geogebra) This resource is on the Integral website in the following sections: MEI FP2 Power series 1, AQA FP3 Series 1, Edexcel FP2 Maclaurin series 1, OCR FP2 Maclaurin
More informationhp calculators HP 9g Statistics Non-Linear Regression Non-Linear Regression Practice Solving Non-Linear Regression Problems
HP 9g Statistics Non-Linear Regression Non-Linear Regression Practice Solving Non-Linear Regression Problems Non-linear regression In addition to the linear regression (described in the HP 9g learning
More informationCOMP 558 lecture 19 Nov. 17, 2010
COMP 558 lecture 9 Nov. 7, 2 Camera calibration To estimate the geometry of 3D scenes, it helps to know the camera parameters, both external and internal. The problem of finding all these parameters is
More informationConvex Functions & Optimization
672 Conve Functions & Optimization Aashray Yadav Abstract - My research paper is based on the recent work in interior-point methods, specifically those methods that keep track of both the primal and dual
More informationECE 250 Data Structures and Algorithms MID-TERM EXAMINATION /5:30-7:00
The examination is out of 64 marks. ECE 250 Data Structures and Algorithms MID-TERM EXAMINATION 2008-2-13/5:30-7:00 Instructions: No aides. Turn off all electronic media and store them under your desk.
More informationRobot Mapping. Least Squares Approach to SLAM. Cyrill Stachniss
Robot Mapping Least Squares Approach to SLAM Cyrill Stachniss 1 Three Main SLAM Paradigms Kalman filter Particle filter Graphbased least squares approach to SLAM 2 Least Squares in General Approach for
More informationGraphbased. Kalman filter. Particle filter. Three Main SLAM Paradigms. Robot Mapping. Least Squares Approach to SLAM. Least Squares in General
Robot Mapping Three Main SLAM Paradigms Least Squares Approach to SLAM Kalman filter Particle filter Graphbased Cyrill Stachniss least squares approach to SLAM 1 2 Least Squares in General! Approach for
More informationMATH 2650/ Intro to Scientific Computation - Fall Lab 1: Starting with MATLAB. Script Files
MATH 2650/3670 - Intro to Scientific Computation - Fall 2017 Lab 1: Starting with MATLAB. Script Files Content - Overview of Course Objectives - Use of MATLAB windows; the Command Window - Arithmetic operations
More informationCS 221 Lecture. Tuesday, 4 October There are 10 kinds of people in this world: those who know how to count in binary, and those who don t.
CS 221 Lecture Tuesday, 4 October 2011 There are 10 kinds of people in this world: those who know how to count in binary, and those who don t. Today s Agenda 1. Announcements 2. You Can Define New Functions
More informationThe Interpolating Polynomial
Math 45 Linear Algebra David Arnold David-Arnold@Eureka.redwoods.cc.ca.us Abstract A polynomial that passes through a given set of data points is called an interpolating polynomial. In this exercise you
More informationx = 12 x = 12 1x = 16
2.2 - The Inverse of a Matrix We've seen how to add matrices, multiply them by scalars, subtract them, and multiply one matrix by another. The question naturally arises: Can we divide one matrix by another?
More informationLecture 9. Curve fitting. Interpolation. Lecture in Numerical Methods from 28. April 2015 UVT. Lecture 9. Numerical. Interpolation his o
Curve fitting. Lecture in Methods from 28. April 2015 to ity Interpolation FIGURE A S Splines Piecewise relat UVT Agenda of today s lecture 1 Interpolation Idea 2 3 4 5 6 Splines Piecewise Interpolation
More informationNumerical Integration
Numerical Integration Numerical Integration is the process of computing the value of a definite integral, when the values of the integrand function, are given at some tabular points. As in the case of
More informationPreliminary Investigations on Resilient Parallel Numerical Linear Algebra Solvers
SIAM EX14 Workshop July 7, Chicago - IL reliminary Investigations on Resilient arallel Numerical Linear Algebra Solvers HieACS Inria roject Joint Inria-CERFACS lab INRIA Bordeaux Sud-Ouest Luc Giraud joint
More informationUniversity of Toronto Faculty of Applied Science and Engineering Edward S. Rogers Sr. Department of Electrical and Computer Engineering
University of Toronto Faculty of Applied Science and Engineering Edward S. Rogers Sr. Department of Electrical and Computer Engineering Final Eamination ECE 4F - Digital Systems Eaminers: S. Brown, J.
More informationA Study of Numerical Methods for Simultaneous Equations
A Study of Numerical Methods for Simultaneous Equations Er. Chandan Krishna Mukherjee B.Sc.Engg., ME, MBA Asstt. Prof. ( Mechanical ), SSBT s College of Engg. & Tech., Jalgaon, Maharashtra Abstract: -
More informationMA 323 Geometric Modelling Course Notes: Day 10 Higher Order Polynomial Curves
MA 323 Geometric Modelling Course Notes: Day 10 Higher Order Polynomial Curves David L. Finn December 14th, 2004 Yesterday, we introduced quintic Hermite curves as a higher order variant of cubic Hermite
More informationPre-Calculus 11: Final Review
Pre-Calculus 11 Name: Block: FORMULAS Sequences and Series Pre-Calculus 11: Final Review Arithmetic: = + 1 = + or = 2 + 1 Geometric: = = or = Infinite geometric: = Trigonometry sin= cos= tan= Sine Law:
More informationECE 250 Algorithms and Data Structures
ECE 250 Algorithms and Data Structures Sections 001 and 002 FINAL EXAMINATION Douglas Wilhelm Harder dwharder@uwaterloo.ca EIT 4018 x37023 2014-04-16T09:00P2H30M Rooms: PAC 7, 8 If you are writing a supplemental
More informationModule 3 Graphing and Optimization
Module 3 Graphing and Optimization One of the most important applications of calculus to real-world problems is in the area of optimization. We will utilize the knowledge gained in the previous chapter,
More informationAMS526: Numerical Analysis I (Numerical Linear Algebra)
AMS526: Numerical Analysis I (Numerical Linear Algebra) Lecture 1: Course Overview; Matrix Multiplication Xiangmin Jiao Stony Brook University Xiangmin Jiao Numerical Analysis I 1 / 21 Outline 1 Course
More informationMaximizing an interpolating quadratic
Week 11: Monday, Apr 9 Maximizing an interpolating quadratic Suppose that a function f is evaluated on a reasonably fine, uniform mesh {x i } n i=0 with spacing h = x i+1 x i. How can we find any local
More information(ii) Use Simpson s rule with two strips to find an approximation to Use your answers to parts (i) and (ii) to show that ln 2.
C umerical Methods. June 00 qu. 6 (i) Show by calculation that the equation tan = 0, where is measured in radians, has a root between.0 and.. [] Use the iteration formula n+ = tan + n with a suitable starting
More informationExample 1: Given below is the graph of the quadratic function f. Use the function and its graph to find the following: Outputs
Quadratic Functions: - functions defined by quadratic epressions (a 2 + b + c) o the degree of a quadratic function is ALWAYS 2 - the most common way to write a quadratic function (and the way we have
More informationPolynomials tend to oscillate (wiggle) a lot, even when our true function does not.
AMSC/CMSC 460 Computational Methods, Fall 2007 UNIT 2: Spline Approximations Dianne P O Leary c 2001, 2002, 2007 Piecewise polynomial interpolation Piecewise polynomial interpolation Read: Chapter 3 Skip:
More informationInstructor: Virginia Davis Course: Foundations for College Math (1)
5/19/01 Final Eam Review Ch 10,11-Virginia Davis Student: Date: Instructor: Virginia Davis Course: Foundations for College Math (1) Assignment: Final Eam Review Ch 10,11 1. Simplif b factoring. Assume
More informationThe Department of Engineering Science The University of Auckland Welcome to ENGGEN 131 Engineering Computation and Software Development
The Department of Engineering Science The University of Auckland Welcome to ENGGEN 131 Engineering Computation and Software Development Chapter 1 An Introduction to MATLAB Course Information (from Course
More informationMatrix Representations
CONDENSED LESSON 6. Matri Representations In this lesson, ou Represent closed sstems with transition diagrams and transition matrices Use matrices to organize information Sandra works at a da-care center.
More informationChapter One. Numerical Algorithms
Chapter One Numerical Algorithms The word algorithm derives from the name of the Persian mathematician (Abu Ja far Muhammad ibn Musa) Al- Khwarizmi who lived from about 790 CE to about 840 CE. He wrote
More informationCS273 Midterm Exam Introduction to Machine Learning: Winter 2015 Tuesday February 10th, 2014
CS273 Midterm Eam Introduction to Machine Learning: Winter 2015 Tuesday February 10th, 2014 Your name: Your UCINetID (e.g., myname@uci.edu): Your seat (row and number): Total time is 80 minutes. READ THE
More informationMini-Lecture 8.1 Introduction to Radicals
Copyright 01 Pearson Education, Inc. Mini-Lecture 8.1 Introduction to Radicals 1. Find square roots.. Find cube roots.. Find nth roots.. Approimate square roots.. Simplify radicals containing variables.
More informationComputational Methods CMSC/AMSC/MAPL 460. Vectors, Matrices, Linear Systems, LU Decomposition, Ramani Duraiswami, Dept. of Computer Science
Computational Methods CMSC/AMSC/MAPL 460 Vectors, Matrices, Linear Systems, LU Decomposition, Ramani Duraiswami, Dept. of Computer Science Some special matrices Matlab code How many operations and memory
More informationChapter 3: Arithmetic for Computers
Chapter 3: Arithmetic for Computers Objectives Signed and Unsigned Numbers Addition and Subtraction Multiplication and Division Floating Point Computer Architecture CS 35101-002 2 The Binary Numbering
More informationGraphics calculator instructions
Graphics calculator instructions Contents: A Basic calculations B Basic functions C Secondary function and alpha keys D Memory E Lists F Statistical graphs G Working with functions H Two variable analysis
More informationFINAL EXAM (PRACTICE A) MATH 265
UNIVERSITY OF CALGARY FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS & STATISTICS FINAL EXAM (PRACTICE A) MATH 265 NAME STUDENT ID EXAMINATION RULES 1. This is a closed book eamination. 2. Calculators are
More informationLesson 6a Exponents and Rational Functions
Lesson 6a Eponents and Rational Functions In this lesson, we put quadratics aside for the most part (not entirely) in this lesson and move to a study of eponents and rational functions. The rules of eponents
More informationTABLE OF CONTENTS CHAPTER 1 LIMIT AND CONTINUITY... 26
TABLE OF CONTENTS CHAPTER LIMIT AND CONTINUITY... LECTURE 0- BASIC ALGEBRAIC EXPRESSIONS AND SOLVING EQUATIONS... LECTURE 0- INTRODUCTION TO FUNCTIONS... 9 LECTURE 0- EXPONENTIAL AND LOGARITHMIC FUNCTIONS...
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Lecture - 24
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Lecture - 24 So in today s class, we will look at quadrilateral elements; and we will
More informationA New Look at Multivariable Interpolation
Page 1 A New Look at Multivariable Interpolation By Namir Shammas Introduction Interpolation using a single independent variable usually involves using legacy algorithm such as the Lagrangian Interpolation,
More informationCSE 547: Machine Learning for Big Data Spring Problem Set 2. Please read the homework submission policies.
CSE 547: Machine Learning for Big Data Spring 2019 Problem Set 2 Please read the homework submission policies. 1 Principal Component Analysis and Reconstruction (25 points) Let s do PCA and reconstruct
More informationApproximating Square Roots
Math 560 Fall 04 Approximating Square Roots Dallas Foster University of Utah u0809485 December 04 The history of approximating square roots is one of the oldest examples of numerical approximations found.
More information