Description

Conditioning number of a linear system
1. a) Solve the following linear system:
400 201
:
800 401
b) Solve the linear system obtained by changing an element of the coe¢ cientmatrix:
401 201
:
800 401
c) Find the conditioning number. (Use Matlab function cond:) 2. Consider the system:
with
and :
a) Solve this system and nd its conditioning number. (Use Matlab func-
tion cond:)
b) Solve the system
Ax~ = ~b;
where
:
Compute the input relative error and the output relative error .
Compute
c) Solve the system
Ax = b;
with
:
Compute the input relative error and the output relative error
. Compute :
3. Find the conditioning numbers of the Hilbert matrices
with hij = i+j1 1; for n = 10 : 15:
4. a) Find the conditioning numbers of the Vandermonde matrices V (tk)

for the points tk = k1; k = 1;n; for n = 10;15.
b) Find the conditioning numbers of the Vandermonde matrices V (tk) for
the points with k = 1;n; for n = 10;15.
2