IAM 961 HW #4

Problem 1. Trefethen & Bau exercise 15.1

Problem 2. Show that matrix-vector multiplication $y_i = \sum_{j=1}^n A_{ij} x_j$ is backward stable when computed with floating-point operations that satisfy the fundamental axioms of floating-point arithmetic. You can use the backwards stability of floating-point computation of the inner product between two vectors.