### 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:

- 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? - We know that you can multiply matrices in
*O(n*operations if and only if you can invert matrices in^{ω})*O(n*operations.^{ω})

True or false: You can multiply matrices in*O(n*operations for any^{ω + ε})*ε > 0*if and only if you can invert matrices "stably'' in*O(n*operations for any^{ω + ε})*ε > 0*.