NDLI: Modeling of linear algebra system with the Fourier transform

Content Provider	IEEE Xplore Digital Library
Author	Jeric̆ević, Z. Koz̆ar, I. Pecak, T.
Copyright Year	2010
Description	Author affiliation: Department of Computer Modeling, Civil Engineering Faculty, Viktora Cara Emina 5, Rijeka, 51000, Croatia (Koz̆ar, I.; Pecak, T.) \|\| Department of Computer Engineering, Engineering Faculty, Vukovarska 58, Rijeka, 51000, Croatia (Jeric̆ević, Z.)
Abstract	Solving dense linear system represented by square matrix of size N requires $O(N^{3})$ operations. We developed procedures for modeling and computation of approximate solutions for problems which are too large to be solved routinely and for which an approximate solution is acceptable. The original dense system is Fourier transformed and then pruned off by removing the insignificant frequencies in accord with the rules of matrix algebra. This approach reduces the original system size and leads to a fast, approximate solutions of eigenvalue or linear system of equations problems. In order to increase flexibility of this approach, the partitioning of input matrix was also tested. The partitioning allows the use of mixed approach where part of the matrix is transformed and reduced in size, while other part is kept intact and in original domain. The examples analyzed were from theoretical chemistry and structural engineering calculations. The quality of solutions for practical problems is demonstrated.
Starting Page	198
Ending Page	202
File Size	256731
Page Count	5
File Format	PDF
ISBN	9781424477630
e-ISBN	9789532330502
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-05-24
Publisher Place	Croatia
Access Restriction	Subscribed
Rights Holder	MIPRO
Subject Keyword	Linear systems Fourier transforms Chemistry Computational modeling Linear algebra Frequency Matrices Eigenvalues and eigenfunctions Equations Testing
Content Type	Text
Resource Type	Article

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