In a previous paper the author presented an extension of an iterative approximate orthogonalization algorithm, due to Z. Kovarik, for arbitrary rectangular matrices. In this algorithm, as Kovarik already observed in his paper, at each iteration an inversion of a symmetric and positive definite matrix is made. The dimension of this matrix equals the number of rows of the initial one, thus the inverse computation can be very expensive. In the present paper we describe an algorithm in which the above matrix inversion step is replaced by an arbitrary odd degree polynomial matrix expression. We prove that this new algorithm converges to the same matrix as the original Kovarik's method. Some numerical experiments described in the last section of the paper show us that, even for small degree polynomial expressions the convergence properties of the new algorithm are comparable with those of the original one.
Modified Kovarik Algorithm For Approximate Orthogonalization Of Arbitrary Matrices
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.