5627: HW1

Define all the terms in Thm 1.2.3

Lower triangular solve.

Define a small test problem for the lower traingular solver algorithm in 1.3.3.  Work your test problem by hand.

Write a function "LowerTSolve[G,b]" in your favorite software that takes a lower triangular matrix G and a vector b and returns the solution following algorithm 1.3.3. You do not need to test for division by zero or for G being lower triangular.

Test your code on your small hand example. Test your code on at least 5 randomly generated examples. Show the results.

Produce a log-log plot of the time for your algorithm on a range of sizes with a comparison line at the theoretical op count slope.

Produce a log-log plot of the time for the built-in linear solve on a range of sizes with a comparison line at the theoretical op count slope. Comment!