Parallel LU decomposition for corner sparse matrix based on FPGA

Abstract

Aiming at the characteristics that corner-block sparse matrix is capable of parallel computing, the invention provides a parallel LU decomposition for corner sparse matrix based on FPGA. a simulating-sorting module, a symbol resolution module and a parallel numerical LU decomposition module form a three-layer processing platform structure consisting of, wherein the parallel numerical LU decomposition module is used for executing the parallel LU decomposition to matrix data and is positioned at the tail end of a whole processing structure; the symbol decomposition module is used for marking the position of an element to be modified in the matrix and is positioned at the middle end of the whole processing structure; and the simulating-sorting algorithm module is used for determining the elimination order of the matrix and is positioned at the foremost end of the whole processing structure; and the three modules are connected through a shared memory unit. The decomposition has the advantage of executing parallel LU decomposition to the corner sparse matrix in real time, can greatly save development cost as compared with the prior art using parallel computers and distributed computers, and can be applied to the field of real-time electrical network analysis.

Description

technical field [0001] The invention belongs to the technical field of data processing, relates to a parallel LU decomposer, and is suitable for parallel LU decomposition of a bordered-diagonal-block sparse matrix (Bordered-Diagonal-Block). Background technique [0002] Corner block sparse matrix is ​​widely used in electronic network design, power system optimization design, graph theory and other science and technology and engineering fields. The solution of sparse linear equations is the core problem in many fields of science and technology. If it is necessary to solve the different right-hand vector b multiple times while the matrix A remains unchanged, the matrix LU decomposition method will significantly save computing time. And the matrix LU decomposition method can take advantage of the sparsity of the matrix and save a lot of storage space, so this method is suitable for solving large sparse matrix problems. [0003] At present, some supercomputers and distributed ...

AI Technical Summary

Problems solved by technology

The implementation of NIOS core programming using FPGA has great flexibility, but the execution efficiency is low, the execution speed is slow and the stability is poor.

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