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 will be presented. The algorithm is considered for the 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 the Woodbury‘s formula. For the problem on an n n grid, the VLSI algorithm needs an area A = O(n2log2n) and the time T = O(nlogn). The global AT 2–complexity of this method is AT 2 = O(n4log4n). 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.