QR factorization of first i columns of A. Suppose the n×k matr... | Filo

SOLVED: In this exercise, you will prove stability of QR factorisation. You can hide factors depending on m and n in the stability calculations. Let ε denote the machine precision.- Let x=(x1, …, xm) be a vector and consider the Householder transformation corresponding to it, i.e., let v be the unit vector along x sign(x1)x e1. Suppose we compute a unit vector ṽ instead. Show that ṽ-v=O(ε).- Let x, v, ṽ be as above, and let y be a vector of length m. We would like to compute b=y-2v, but we use ṽ

If A is symmetric, show that each matrix A_{k} in the QR-algori... | Filo

Answered: 2 2 4 3 Apply one iteration of the QR algorithm to the matrix A given in (a) with shift µ = 5 | bartleby