## Stanford 50: State of the Art and Future Directions of Computational Mathematics and Numerical Computing  ### Information

• March 31, 2007
• 2:00 pm - 2:25 pm

# Suggested extra credit questions for a future edition of Golub & Van Loan

##### Jim Demmel (UC Berkeley)

A generation of researchers and students has benefitted immensely from the textbook "Matrix Computations'' by Gene Golub and Charlie Van Loan. In this talk we imagine what a set of "extra credit'' questions for a future edition might look like. Here are two examples for section 2.4:

1. You have an array of n double precision (64-bit) floating point numbers, and are allowed to do n-1 double extended (80-bit) floating point additions to compute their sum (and no other arithmetic operations or "bit-fiddling''). How small can you make the error bound?
2. We know that you can multiply matrices in O(nω) operations if and only if you can invert matrices in O(nω) operations.
True or false: You can multiply matrices in O(nω + ε) operations for any ε > 0 if and only if you can invert matrices "stably'' in O(nω + ε) operations for any ε > 0.