Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Analysis I
(2nd Homework Assignment)
Exercise 5 (Block Gauss elimination)
Let A RN N , N :=
structured according to
A=
A11
A21
Am1
m
i=1
ni , ni N , 1 i m
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Analysis I
(3rd Practical Homework Assignment)
Practical Exercise 3 (Linear Least Squares Problem)
Write a code which implements the linear least squares
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Analysis I
(2nd Practical Homework Assignment)
Practical Exdercise 2 (cg method)
The deection u = u(x) , x = (x1 , x2 )T := (0, 1)2 of a clamped membrane
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Mathematics I
(10. Homework Assignment)
Exercise 34 (L2estimate for piecewise linear interpolation)
The interpolation error estimates presented in class
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Mathematics I
(9. Homework Assignment)
Exercise 30 (Perturbation lemma)
Given B lRnn and a submultiplicative matrix norm
Show that the matrix I B is regul
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Mathematics I
(8. Homework Assignment)
Exercise 27 (Regula falsi of higher order)
Assume that f C 1 ([a, c), 0 < a < c, has a simple zero x [a, c] and tha
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Mathematics I
(7. Homework Assignment)
Exercise 25 (L2estimate for piecewise linear interpolation)
The interpolation error estimates presented in class p
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Mathematics I
(6th Homework Assignment)
Exercise 21 (Regula falsi of higher order)
Assume that f C 1 ([a, c), 0 < a < c, has a simple zero x [a, c] and th
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Analysis I
(5th Homework Assignment)
Exercise 17 (Reformulation of linear least squares problems)
Let A Rmn , m > n , rank A = n , b Rm . The linear least
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Analysis I
(4th Homework Assignment)
Exercise 13 (Gradient method and semiiterative Richardson iteration)
Let A Rnn be symmetric positive denite with the
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Analysis I
(3rd Homework Assignment)
Exercise 9 (Convergence of the Jacobi iteration)
A matrix A Rnn is called strongly diagonally dominant, if
 aii  >
Department of Mathematics
University of Houston
Numerical Analysis I
Dr. Ronald H.W. Hoppe
Numerical Mathematics I
(1. Homework Assignment)
Exercise 1 (Gauss elimination for diagonally dominant matrices)
A matrix A Rnn is called diagonally dominant, if

University of Houston, Department of Mathematics
Numerical Analysis, Fall 2005
Chapter 6 Numerical solution of eigenvalue problems
6.1 Theoretical foundations
Denition 6.1 Eigenvalue, eigenvector, spectrum
Let A Cnn. A number C is called an eigenvalue of
University of Houston, Department of Mathematics
Numerical Analysis, Fall 2005
Chapter 5 Numerical integration
Problem: Let f : [a, b] lR lR be a piecewise continuous function.
Compute the integral
b
f (x) dx .
I(f ) =
a
If I(f ) can not be determined in
University of Houston, Department of Mathematics
Numerical Analysis, Fall 2005
4 Interpolation
4.1 Polynomial interpolation
Problem: LetPn(I) , n lN , I := [a, b] lR, be the linear space of polynomials of degree n on I,
Pn(I) := cfw_ pn : I lR  pn(x) =
n
University of Houston, Department of Mathematics
Numerical Analysis, Fall 2005
3 Numerical Solution of Nonlinear Equations and Systems
3.1 Fixed point iteration
Reamrk 3.1 Problem
Given a function F : lRn lRn, compute x lRn such that
()
F(x) = 0 .
In this