How to optimize the multiplication of large matrices in Matlab?

I have 2 matrices A, B, and vector C that I need to multiply. They are fairly large.

Matrix A = 10000x10000

Matrix B = 10000x10000

Vector C = 10000x1

If I perform A*B*C, this takes a long time so I used sparse function which collapses the matrices/vectors by removing large number of zeros then I convert it back to a full matrix.

full(sparse(A)*sparse(B)*sparse(C))

It's faster but I was wondering if there are more efficient techniques for multiplying them together. Would it be better to write for loops?

Secondly, some of the elements in my matrix have values close to zero so I can replace these with zeroes before converting them to sparse matrices. What's the best way to do this?

Answer 1

[James Tursa]

Force the matrix-vector multipy to happen first. E.g.,

A*(B*C)

[John]

Dude, this improved the performance. Thanks!!!

[Ken]

it works really well! surprised!

Answer 2

[Sean de Wolski]

I doubt you'll be able to get anything faster than the highly optimized BLAS libraries that MATLAB uses to perform matrix arithmetic. The only thing I've heard of that might be faster is mtimesx on the FEX and even that, I've never reproduced.

Answer 3

[per isakson]

Your second question:

    A( A < small_number ) = 0;

or better

    A( abs(A) < small_number ) = 0;

[John]

Thanks, does the abs(A) make it faster or more efficient?

[Sean de Wolski]

it makes it so that -25 does not become 0.