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 )
=
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). Af
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 fal
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 fal
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
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 syst
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
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 g
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 quadratur
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.
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 requi
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)
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 g
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 pen
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 t
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
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 syste
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 syst
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 obje
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 syste
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
Univer