MATH 3511 Numerical Analysis 2
Due April 5, 2012
Assignment 8
1. (20 points) In class to approximate derivatives of the function at a point we used the dierence formulas,
that we show to satisfy
u(x +
MATH 3511 Numerical Analysis 2
February 9, 2012
Assignment 4
1. (10 points) Find the permutation matrix P so that P A can be factored into the product LU , where L
is lower triangular with 1s on its d
MATH 3511 Numerical Analysis 2
February 2, 2012
Assignment 3
1. (10 points) Let two matrices A and B commute, i.e. AB = BA. Do AT and B T commute as well?
2. (10 points) Let A be an invertible matrix.
MATH 3511 Numerical Analysis 2
January 26, 2012
Assignment 2
1. (10 points) Perform the following matrix-matrix multiplication.
2
4
5
3
3
2
1
1
0 4
4
0
9
1
2
2. (10 points) Show that the following mat
MATH 3511 Numerical Analysis 2
January 19, 2012
Assignment 1
1. (10 points)
Use Gaussian elimination with backward substitution to solve the following linear systems.
4x1 x2 + x3
2x1 + 5x2 + 2x3
x1 +
MATH 3511 Numerical Analysis 2
February 23, 2012
Assignment 5
1. (10 points) Prove that the following sequences are convergent and nd their limits.
2
(a) xk = k ek , cos k , k 2 + k k
k
T
T
2
k
(b) xk
MATH 3511 Numerical Analysis 2
Due March 20, 2012
Assignment 6
1. (10 points) Show that if
is any natural norm, then
( A1 )1 | A
for any eigenvalue of the nonsingular matrix A.
2. (20 points) Let the
MATH 3511
Numerical Analysis II
Spring 2012
Syllabus
Instructor
Dmitriy Leykekhman
Department of Mathematics
(860) 405-9294
[email protected]
MSB 332
Venue and Time
MSB 219, TuTh 9:30-10:45 pm
MATH 3511
Lecture 2. Matrix Algebra
Dmitriy Leykekhman
Spring 2012
Goals
Matrix-matrix multiplication.
Inverse of a Matrix.
Determinant.
D. Leykekhman - MATH 3511 Numerical Analysis 2
Matrix Algebra
1
MATH 3511 Numerical Analysis 2
Due April 12, 2012
Assignment 9
1. (20 points) For the problem
u (t) = au(t),
a > 0,
u(0) = 1,
the Crank-Nicolson scheme at is dened by
U n+1 U n
U n+1 + U n
= a
,
t
2
U
MATH 3511
Basics of MATLAB
Dmitriy Leykekhman
Spring 2012
Topics
Sources.
Entering Matrices. Basic Operations with Matrices.
Build in Matrices. Build in Scalar and Matrix Functions.
if, while, for
m-l