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

Using the QR factorization defined in Appendix A.12, show that ... | Filo

Problem 3.11: Computing the QR Factorization in MATLAB3.11. Most library routines for computing the QR factorization of an m x n matrix A return the matrix R in the upper triangle of the storage for A and the Householder vectors in the lower triangle of A, with an extra vector to accommodate the overlap on the diagonal. Write a routine that takes this output array and auxiliary vector and forms the orthogonal matrix Q explicitly by multiplying the corresponding sequence of Householder transforma

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