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 + x) u(x x)
u (x) =
+ O(x2 )
2x
and
u(x + x) 2u(x) + 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 diagonal and U is upper triangular for the matrix
0 2 1
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. Show that det (A1 ) = (det A)1 .
3. (10 points) Give a
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 matrix is nonsingular and compute its inverse.
12 0
2 1 1
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 = e k , 1+1 , 1+3+5+k2+(2k1)
k2
1
2. (20 points) Let
3
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 sequence cfw_x(k) dened x(k) = T x(k1) + c for T < 1 c
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.
Ofce hours
Thursday 2:00-3:00 pm or by appointment
Pr
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
Properties of Matrices
A space of all matrices with m
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 0 = 1.
n = 0, 1, 2, .
Show that the Crank-Nicolson sch
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-les
Graphics.
Sparse Matrices.
D. Leykekhman - MATH 3795