Introduction to Computational Linear Algebra

Gauss Elimination and LU Decompositions of Matrices 77

3.8 Computer Exercises

Computer Exercise 3.1 Transform the mylu1 to become mylusym in a way

that the operation:

A(k+1:n,k+1:n)=A(k+1:n,k+1:n)-A(k+1:n,k)*A(k,k+1:n);

is done only on the lower part of the matrix A. Check out the operation count

in the form of O(mn

3

). What is m?

Computer Exercise 3.2 Modify the above function [L,D]=mylusym(A)

to obtain a “simple” MATLAB implementation of Cholesky decomposition:

function B=mychol(A).

Computer Exercise 3.3 Complete the direct Cholesky’s decomposition

function B=mycholdir(A) of Algorithm 3.4 which computes B directly from

A using external products. Find