Le Borne, SabineSabineLe Borne2023-03-312023-03-312023-10Numerical Linear Algebra with Applications 30 (5): e2497 (2023-10)http://hdl.handle.net/11420/15087The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods.en1099-150620235Wileyhttps://creativecommons.org/licenses/by-nc-nd/4.0/block QR factorizationHouseholder methodMathematikJournal Article10.15480/882.503610.1002/nla.249710.15480/882.5036Journal Article