Introduction to Computational Linear Algebra

Basic Linear Algebra Subprograms - BLAS 21

for k=

C( , )=C( , )+v( )*A( , );

end

end

2. Assume A is also an upper triangular matrix. Modify (1.20) to

obtain an algorithm that computes C = A ×B exploiting the special

structures of A and B. Give your answer by filling in the missing spaces

in the following MATLAB program that gives the matrix C column-wise:

function C=MultUpperUpper(A,B)

C=zeros(n,n);

for j=1:n

v=B( ,j);

for k=

C( , )=C( , )+v( )*A( , );

end

end

Give the number of flops needed to execute this algorithm.

Exercise 1.10

Let A and B be square matrices (both stored column-wise) in R

n×n

with B

a Lower Triangular matrix. Consider the formula that gives C = A × B:

C(:, j) = Σ

n

k=1

B(k, j) × A(:, k), j = 1, ..., n (1.21)

1. Use and modify (1.21) to obtain an algorithm ...