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

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/spl times/n grid, the VLSI algorithm needs an area A=O(n/sup 2/log/sup 2/n) and a time T=O(n log n). The global AT/sup 2/-complexity of this method is AT/sup 2/=O(n/sup 4/log/sup 4/n). 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.