An Iterative Algorithm for Approximate Orthogonalisation of Symmetric Matrices

In a previous paper one of the authors presented an extension of an iterative approximate orthogonalisation algorithm, due to Z. Kovarik, for arbitrary rectangular matrices. In the present paper we propose a modified version of this extension, for the class of arbitrary symmetric matrices. For this new algorithm, the computational effort per iteration is much smaller than for the initial one. We prove its convergence and also derive an error reduction factor per iteration. In the second part of the paper we show that we can eliminate the matrix inversion required by the previous algorithm in each iteration, by replacing it with a polynomial matrix expression. Some numerical experiments are also presented for a collocation discretisation of a first kind integral equation.

@article{id447,
  author = {Mohr, M. and Popa, C. and R\"ude, U.},
  doi = {10.1080/00207160310001650134},
  journal = {International Journal of Computer Mathematics},
  language = {en},
  number = {2},
  pages = {215{\textendash}226},
  title = {An Iterative Algorithm for Approximate Orthogonalisation of Symmetric Matrices},
  volume = {81},
  year = {2004},
}

%O Journal Article
%A Mohr, M.
%A Popa, C.
%A Rüde, U.
%R 10.1080/00207160310001650134
%J International Journal of Computer Mathematics
%G en
%N 2
%P 215–226
%T An Iterative Algorithm for Approximate Orthogonalisation of Symmetric Matrices
%V 81
%D 2004