Numerical solution of symmetric leastsquares problems with an inversionfree Kovariktype algorithm
 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 inversefree 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 inversefree variant. We then investigate the application of the new algorithm for the numerical solution of linear leastsquares 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 firstkind integral equation demonstrate a meshindependent behaviour and stability with respect to numerical errors introduced by the use of numerical quadrature.
 BibTeX

@article{id918, author = {Mohr, M. and Popa, C.}, doi = {10.1080/00207160701421151}, journal = {International Journal of Computer Mathematics}, language = {en}, number = {2}, pages = {271286}, title = {Numerical solution of symmetric leastsquares problems with an inversionfree Kovariktype algorithm}, volume = {85}, year = {2008}, }
 EndNote

%O Journal Article %A Mohr, M. %A Popa, C. %R 10.1080/00207160701421151 %J International Journal of Computer Mathematics %G en %N 2 %P 271286 %T Numerical solution of symmetric leastsquares problems with an inversionfree Kovariktype algorithm %V 85 %D 2008