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IMA Journal of Numerical Analysis Advance Access published online on August 21, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp018
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Householder triangularization of a quasimatrix

Lloyd N. Trefethen{dagger}

Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK

{dagger} Email: nick.trefethen{at}comlab.ox.ac.uk

Received on 4 July 2008.


  Abstract

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.

Key Words: Householder triangularization; QR factorization; chebfun; quasimatrix; singular value decomposition


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