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Numerical solution of symmetric least-squares problems with an inversion-free Kovarik-type algorithm

Mohr, M., and C. Popa (2008), Numerical solution of symmetric least-squares problems with an inversion-free Kovarik-type algorithm, International Journal of Computer Mathematics, 85(2), 271-286, doi:10.1080/00207160701421151.

Abstract
In a previous paper we presented two variants of Kovarik's approximate orthogonalisation algorithm for arbitrary symmetric matrices, one with and one without explicit matrix inversion. Here we propose another inverse-free version that has the advantage of a smaller bound on the convergence factor, while the computational costs per iteration are even less than in the initial inverse-free variant.

We then investigate the application of the new algorithm for the numerical solution of linear least-squares problems with a symmetric matrix. The basic idea is to modify the right hand side of the equation during the transformation of the matrix. We prove that the sequence of vectors generated in this way converges to the minimal norm solution of the problem.

Numerical tests with the collocation discretisation of a first-kind integral equation demonstrate a mesh-independent behaviour and stability with respect to numerical errors introduced by the use of numerical quadrature.
BibTeX
@article{id918,
  author = {M. Mohr and C. Popa},
  journal = {International Journal of Computer Mathematics},
  month = {feb},
  number = {2},
  pages = {271-286},
  title = {{Numerical solution of symmetric least-squares problems with an inversion-free Kovarik-type algorithm}},
  volume = {85},
  year = {2008},
  doi = {10.1080/00207160701421151},
}
EndNote
%0 Journal Article
%A Mohr, M.
%A Popa, C.
%D 2008
%N 2
%V 85
%J International Journal of Computer Mathematics
%P 271-286
%T Numerical solution of symmetric least-squares problems with an inversion-free Kovarik-type algorithm
%8 feb
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Printed 12. Dec 2019 06:55