A method for solving an inverse matrix of a symmetric or erbium-density symmetric positive definite matrix

Abstract

The invention provides a method for solving an inverse matrix of a symmetric or erbium-density symmetric positive definite matrix, and aims to provide a solving method which is low in operation precision loss, can improve the Cholesky decomposition parallelism and realizes a high-speed low-delay full parallel structure. The method is realized through the following technical scheme: in the processof solving, a fixed-point number of shift operations are adopted, and a traditional Radit-is used; The lower triangular matrix of the sub-matrix of the Looking structure is converted into a lower triangular matrix of an equivalent sub-matrix; matrix iteration is carried out, n times of iteration is carried out on the n-order matrix A by utilizing a parallel Cholesky decomposition algorithm module,a lower triangular matrix and a diagonal matrix are output, and a divisor decomposition function is achieved on an FPGA (Field Programmable Gate Array) parallel embedded platform in a table look-up manner; In the iteration process, triangular sub-matrix updating, column reduction and diagonal element calculation under the matrix are executed at the same time; And an improved (RL) parallel decomposition algorithm is used to realize a Cholesky decomposition full parallel structure.

Description

technical field [0001] The present invention relates to a kind of occasion that needs to quickly solve the inverse problem involving symmetric (or Hermitian symmetric) positive definite matrix, and the specific application fields mainly include (but not limited to) array signal processing, measurement and control, and solutions in the fields of artificial intelligence Inverse matrix method for symmetric or Hermitian symmetric positive definite matrices. Background technique [0002] With the increasing requirements of computing power and computing speed in various industries, intensive matrix operations are widely used in signal processing and image processing, and parallel computing has become an important research field in computer science today. The inherent complexity, reliability, portability and other problems of the parallel program development process restrict the use and promotion of parallel programs and often require the system to perform real-time calculations, w...

AI Technical Summary

Problems solved by technology

In the traditional Right-Looking structure, the sub-matrix diagonal update process (refresh) that only needs to be added, subtracted, and multiplied must wait for the column reduction process (cdiv) that requires division to be completed first. This dependency will greatly reduce the entire The operation speed of the iterative process (ie formula (4))

And this is where the bottleneck of the traditional Right-Looking structure lies: the multiplication and addition operation with a short processing time needs to wait for the division operation with a long processing cycle, which slows down the running time of the entire algorithm

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