Sample Solutions of HW2 AMS527
March 5, 2014
5.5 (a)
xk1 f (xk ) xk f (xk1 )
f (xk ) f (xk1 )
xk f (xk ) xk f (xk1 ) + xk1 f (xk ) xk f (xk )
=
f (xk ) f (xk1 )
xk (f (xk ) f (xk1 ) f (xk )(xk xk1 )
=
f (xk ) f (xk1 )
xk xk1
= xk f (xk )
f (xk ) f (xk1 )
11
Numerical Solution of Ordinary Dierential
Equations
In this chapter we deal with the numerical solutions of the Cauchy problem
for ordinary dierential equations (henceforth abbreviated by ODEs). After
a brief review of basic notions about ODEs, we intr
AMS527: Numerical Analysis II
Runge-Kutta Methods
Xiangmin Jiao
SUNY Stony Brook
Xiangmin Jiao SUNY Stony Brook
AMS527: Numerical Analysis II
1 / 11
General Form of Runge-Kutta Methods
uk+1 = uk + hF (tn , un , h; f ),
n 0,
where
s
F (tn , un , h; f ) =
b
AMS 527 Sample Test 1
March 5, 2014
Note: The exams are closed-book. A one-page cheat sheet is allowed, but you must prepare the it yourself.
1. Answer whether the following statements are true or false and give a brief explanation.
(a) The choice of algo
AMS 527 Sample Test 1
March 9, 2014
Note: The exams are closed-book. A one-page cheat sheet is allowed, but you must prepare the it yourself.
1. Answer whether the following statements are true or false and give a brief explanation.
(a) The choice of algo
AMS 527 Sample Final Exam
May 9, 2014
1. Answer whether the following statements are true or false and give a brief explanation.
(a) A small residual f (x) guarantees an accurate solution of a system of nonlinear equations f (x) =
0.
False. The error depe
AMS 527 Sample Final Exam
April 26, 2014
1. Answer whether the following statements are true or false and give a brief explanation.
(a) A small residual f (x) guarantees an accurate solution of a system of nonlinear equations f (x) =
0.
(b) When minimizin
AMS527: Numerical Analysis II
Review for Final Exam
Xiangmin Jiao
SUNY Stony Brook
Xiangmin Jiao SUNY Stony Brook
AMS527: Numerical Analysis II
1/8
Announcements
Final exam will be on Tuesday 5/13 at 8:3011:00pm in Light
Engineering 154
The exam will be a
AMS 527 Sample Test 2
April 2, 2014
1. Answer whether the following statements are true or false and give a brief explanation.
(a) When using the same number of nodes, Gaussian quadrature rule is in general more accurate than
Newton-Cotes quadrature rule.
AMS 527: Solutions to Sample Test 2
April 9, 2014
1. Answer whether the following statements are true or false and give a brief explanation.
(a) When using the same number of nodes, Gaussian quadrature rule is in general more accurate than
Newton-Cotes qu
SIAM J. NUMER. ANAL.
() 1980 Society for Industrial and Applied Mathematics
Vol. 17, No. 2, April 1980
0036-1429/80/1702-0005 $01.00/0
MONOTONE PIECEWISE CUBIC INTERPOLATION*
F. N. FRITSCHt
AND
R. E. CARLSON
Abstract. Necessary and sufficient conditions a
AMS 527, Spring 2015, Homework 6 Sample Solution
Electronic submission of homework assignments is strongly encouraged for the computer problems. For
the written part, you are encouraged (but not required) to typeset using LATEX or LYX (an easy-to-use
fron
AMS 527, Spring 2015, Homework 5
100 points.
Electronic submission of homework assignments is strongly encouraged for the computer problems. For
the written part, you are encouraged (but not required) to typeset using LATEX or LYX (an easy-to-use
front-en
AMS 527: Solutions to Sample Test 2
1. Answer whether the following statements are true or false and give a brief explanation.
(a) When using the same number of nodes, Gaussian quadrature rule is in general more accurate than
Newton-Cotes quadrature rule.
Sample Solutions of HW3 AMS527
6.16 (a) The Jacobian J g (x, y) vanishes (i.e., the constraint set has a cusp) at the solution (1, 0), and thus
the Lagrange multipliers do not exist. (b) Using the penalty method, we minimize the unconstrained
function
1
Sample Solutions of AMS527 HW4
1. (a) In one subinterval [a, b], we have
M (f )
=
T (f )
=
f 00 (m)
(b a)3 + O(b a)5 ),
24
f 0 (m)
I(f ) +
(b a)3 + O(b a)5 ).
8
I(f )
Since f 00 (x) 0, this implies that in each subinterval we have
M (f ) I(f ) T (f ).
Su
AMS 527 Sample Test 1
Note: The exams are closed-book. A one-page cheat sheet is allowed, but you must prepare the it yourself.
1. Answer whether the following statements are true or false and give a brief explanation.
(a) The choice of algorithm for solv
AMS 527, Spring 2014, Homework 7 Sample Solution
1. (15 points) Exercise 11.1 on page 489 of Heath book.
Suppose you are given a general-purpose subroutine for solving initial value problems for systems of
n first order ODEs y 0 = f (t, y), and this is th
AMS 527 Sample Final Exam
May 11, 2015
1. Answer whether the following statements are true or false and give a brief explanation.
(a) A small residual kf (x)k guarantees an accurate solution of a system of nonlinear equations f (x) =
0.
False. The error d
AMS527: Numerical Analysis II
Linear Programming
Xiangmin Jiao
SUNY Stony Brook
Xiangmin Jiao (SUNY Stony Brook)
AMS527: Numerical Analysis II
1/8
Linear Programming
Linear programming has linear objective function and linear equality
and inequality const
AMS 527, Spring 2014, Homework 7 Sample Solution
1. (15 points) Exercise 11.1 on page 489 of Heath book.
Suppose you are given a general-purpose subroutine for solving initial value problems for systems of
n rst order ODEs y = f (t, y), and this is the on
Ordinary Differential Equations
Numerical Solution of ODEs
Additional Numerical Methods
Scientic Computing: An Introductory Survey
Chapter 9 Initial Value Problems for
Ordinary Differential Equations
Prof. Michael T. Heath
Department of Computer Science
U
Discrete Fourier Transform
Fast Fourier Transform
Applications
Scientic Computing: An Introductory Survey
Chapter 12 Fast Fourier Transform
Prof. Michael T. Heath
Department of Computer Science
University of Illinois at Urbana-Champaign
Copyright c 2002.