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Method of column pivoting LU decomposition based on FPGA

A main processing unit and column number technology, applied in the field of matrix LU decomposition, can solve problems such as calculation accuracy defects

Inactive Publication Date: 2009-12-16
NAT UNIV OF DEFENSE TECH
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Problems solved by technology

[0006] The technical problem to be solved in the present invention is: in order to avoid the defects of LU decomposition without pivoting in terms of calculation accuracy, a method of LU decomposition based on column selection of pivots is proposed to reduce the time complexity of LU decomposition, thereby speeding up the process of dense matrix Solving Systems of Linear Equations

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[0066] specific implementation plan

[0067] figure 1 Is the overall flow chart of the present invention. Firstly, a FPGA-based master-slave parallel computing system is constructed. The master-slave parallel computing system consists of a master processing unit and P slave processing units. Then the master-slave parallel computing system treats the decomposition matrix A(a i，j , 1≤i, j≤M, and M is a positive integer) for column selection pivot LU decomposition:

[0068] 1. The global state control module of the main processing unit initializes the parameter M'=M according to the size M of the matrix to be processed currently. Matrix to be decomposed A'=A.

[0069] 2. The parameter sending module of the master processing unit sends the parameter M' to the first slave processing unit. The external memory controller of the main processing unit fetches the matrix A' to be decomposed from the external memory by columns (a i，j , 1≤i, j≤M), sent by the data sending module to t...

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Abstract

The invention discloses a method of column pivoting LU decomposition based on FPGA, the technical problem to be solved is to reduce time complexity of LU decomposition and accelerate solving of dense matrix linear equation system. The technical solution comprises that: at first a FPGA-based master-slave parallel computation system composed of a master processing unit and P slave processing units is constructed, the master-slave parallel computation system carries out column pivoting LU decomposition on the matrix to be decomposed, the master processing unit sends parameters and the matrix to be decomposed to a first slave processing unit, the slave processing unit processes the matrix in a pipeline way, and the processing result is sent to the master processing unit from the P slave processing unit. Computation accuracy is dramatically improved in contrast to non-pivoting LU decomposition with the invention being used, computing speed is high, and the master-slave parallel computation system thereof has expandability.

Description

technical field [0001] The invention relates to a matrix LU (Lower / Upper triangular) decomposition method, in particular to an FPGA-based dense matrix (generally a square matrix with equal rows and columns) column-selected pivot LU decomposition method. Background technique [0002] Solving dense linear equations plays an important role in the fields of scientific computing and high-performance computing, and dense matrix LU decomposition (abbreviated as LU decomposition) is an important step in solving dense linear equations, and it is the most critical step that affects the performance of dense linear equations. The time complexity of LU decomposition is high, about (2 / 3)n 3 , which accounts for most of the running time of the system of linear equations. LU decomposition is divided into pivoting LU decomposition and non-pivoting LU decomposition (the most common pivoting LU decomposition is column-selecting pivot LU decomposition). Among them, LU decomposition without piv...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/11G06F17/16
Inventor 邬贵明窦勇夏飞姜晶菲周杰
Owner NAT UNIV OF DEFENSE TECH
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