Original scientific paper

Approximate solution of dense linear systems

Željko Jeričević

Abstract

A novel numerical approach for approximate solution of large linear systems of a dense type has been developed. The method is based on Fourier transform although any unitary, orthogonal transform which concentrates energy in a small number of coefficients can be used. The idea comes from digital signal processing where pruning off insignificant information from spectra or filtering of selected information in frequency domain is usual practice. The procedure is to transform the linear system from the time and space domain to the frequency domain, generating a transformed system. The least significant portions in the transformed system are deleted as the whole rows and columns, yielding a smaller pruned system. The pruned system is solved in the frequency domain, generating the transform of approximate solution. Inverting the transform of approximate solution yields the approximate solution of original system. Numerical experiments illustrating feasibility of the method and quality of the approximation for 1000 by 1000 eigenvalue problem in chemical graph theory are presented.

Keywords

Fourier; linear system; approximate solution; eigenvalue problem; distance matrix; nanotube

Hrčak ID:

2550

URI

https://hrcak.srce.hr/2550

Publication date:

20.12.2005.

Article data in other languages: croatian

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