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A least square solution method of a time-varying overdetermined linear equation group

A technology of linear equations and least squares, applied in complex mathematical operations, etc., can solve problems such as inefficiency, accuracy and stability, and achieve the effects of good practicability, strong robustness, and fast convergence speed

Inactive Publication Date: 2019-03-29
SOUTH CHINA UNIV OF TECH
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  • Description
  • Claims
  • Application Information

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Problems solved by technology

This means that when these methods are directly applied to time-varying systems, they may not be efficient, accurate and stable enough

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  • A least square solution method of a time-varying overdetermined linear equation group
  • A least square solution method of a time-varying overdetermined linear equation group
  • A least square solution method of a time-varying overdetermined linear equation group

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Embodiment

[0040] This embodiment provides a method for solving the least squares solution of time-varying overdetermined linear equations, the process of the method is as follows figure 1 shown, including the following steps:

[0041] 1) Convert time-varying overdetermined linear equations into time-varying matrix equations;

[0042] 2) the time-varying matrix equation of step 1) is converted into corresponding normal equations;

[0043] 3) provide the error monitoring function of the normal equations of step 2), and convert the solution of the normal equations into the optimization problem;

[0044] 4) According to the neurodynamic design method, the neurodynamic design of the corresponding strain parameters is given;

[0045] 5) Substituting the error monitoring function in step 3), transforming the variable parameter neural dynamics design obtained in step 4) into a variable parameter convergent differential neural network solver, and solving the optimization problem in step 3).

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Abstract

The invention discloses a least square solution method of a time-varying overdetermined linear equation group, comprising the following steps: 1) converting the time-varying overdetermined linear equation group into a time-varying matrix equation; 2) converting the time-varying matrix equation of the step 1) into a corresponding normal equation group; 3) the error monitoring function of the normalequation system of the step 2) is given, and the solution of the normal equation system is converted into the solution of the optimization problem; 4) according to that neurodynamic design method, the strain parameter neurodynamic design is given; 5) substituting the error monitoring function of the step 3), converting the variable parameter neurodynamic design obtained in the step 4) into a variable parameter convergent differential neural network solver, and solving the optimization problem of the step 3). The method has the advantages of faster convergence speed, stronger robustness, higher convergence accuracy and better practicability, which is based on neurodynamics to solve the time-varying overdetermined linear equations.

Description

technical field [0001] The invention relates to the field of solving time-varying overdetermined linear equations, in particular to a method for solving least squares solutions of time-varying overdetermined linear equations based on neural dynamics. Background technique [0002] The time-varying overdetermined linear equation system refers to the linear equation system whose number of linear constraint equations is greater than the number of free variables. In most cases, the exact solution cannot be solved, so the least squares solution is usually solved. Solving overdetermined linear equations is widely used in linear regression problems, Steklov eigenvalue problems, wireless communication problems, etc. The problem of finding the least squares solution of a general time-varying overdetermined linear equation system can be described as: [0003] [0004] The dimension of the equation system satisfies that the number m of the equation system is greater than the number ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/12
CPCG06F17/12
Inventor 张智军邱泰儒郑陆楠
Owner SOUTH CHINA UNIV OF TECH
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