CS 311 Assignment 8

1. Give a backward error analysis showing that the floating point dot product of two vectors dot(a,b) = Σ_i=1,…,d (a_i b_i) is the exact dot product of two perturbed vectors.
2. Add the Gauss-Seidel algorithm to jacobi.c and test the v-cycle using Gauss-Seidel instead of Jacobi as a smoothing step. How does the choice of smoother affect the number of smoothing steps and the number V cycles performed for convergence?