A method for improving orthogonality of rows and columns of matrices

Abstract

In [5] Kovarik described a method for approximate orthogonalization of a finite set of linearly independent vectors from an arbitrary Hubert space. In this paper we generalize this method to the case when the vectors are rows (not necessary linearly independent) of an arbitrary rectangular real matrix. In this case we prove that, after the application of Kovarik's algorithm, both rows and columns of the matrix are transformed in vectors which are “quasi-orthogonal”, in a sense that is clearly described. Some numerical experiments, on a matrix obtained from the discretization of a first kind integral equation are presented in the last section of the paper.

Keywords:

• Approximate orthogonalization methods
• Rectangular matrices

AMS Subject Classifications::

• 65F10
• 65F20

C.R. Category::

• G1.3

^∗ [email protected]

^∗ [email protected]

Notes

^∗ [email protected]