Householder triangularization of a quasimatrix

摘要

A standard algorithm for computing the QR factorization of a matrix A is Householder triangularization. Here this idea is generalized to the situation in which A is a quasimatrix, that is, a ‘matrix’ whose ‘columns’ are functions defined on an interval [a, b]. Applications are mentioned to quasimatrix least squares fitting, singular value decomposition and determination of ranks, norms and condition numbers, and numerical illustrations are presented using the chebfun system.