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A direct block-five-diagonal system solver for the VLSI parallel model

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1 Author(s)
M. Vajtersic ; Inst. for Inf., Slovak Acad. of Sci., Bratislava, Slovakia

A VLSI algorithm for solving a special block-five-diagonal system of linear algebraic equations is presented. The algorithm is considered for a VLSI parallel computational model where both the time of the algorithm and the area of its design are components of the complexity estimations. The linear system arises from the finite-difference approximation of the first biharmonic boundary value problem. The algorithm computes the solution by a direct method based on Woodbury's formula (see G.H. Golub and C.F. Van Loan, “Matrix Computations”, Johns Hopkins Univ. Press, Baltimore, 1989). For the problem on an n×n grid, the VLSI algorithm needs an area A=O(n 2log2n) and a time T=O(n log n). The global AT2-complexity of this method is AT2=O(n4 log4n). This result represents the best upper bound for solving this problem in VLSI. Moreover, this algorithmic design could serve as a preliminary step towards the analysis and development of more detailed structures of specialized VLSI computer devices for solving the biharmonic problem

Published in:

Parallel Processing Symposium, 1996., Proceedings of IPPS '96, The 10th International

Date of Conference:

15-19 Apr 1996