Method and system for accurately and effectively solving eigenstate of large sparse matrix

A sparse matrix and eigenstate technology, applied in the field of engineering calculations, can solve problems such as large dependence on initial values ​​and low convergence speed, and achieve the effects of reducing dependence, increasing convergence speed, and improving iterative solution efficiency

Pending Publication Date: 2020-04-21
JIAXING UNIV
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Problems solved by technology

The solution to the eigenstates of this method is an iterative solution process, which can be self-adjusted for iterative solutions after an initial parameter is given, which solves the problem that the existing eigenstate solutions have a large dependence on the initial value and low convergence speed

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  • Method and system for accurately and effectively solving eigenstate of large sparse matrix
  • Method and system for accurately and effectively solving eigenstate of large sparse matrix
  • Method and system for accurately and effectively solving eigenstate of large sparse matrix

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Embodiment Construction

[0030] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

[0031] On the one hand, see attached figure 1 , the embodiment of the present invention discloses an accurate and effective method for solving the eigenstates of a large sparse matrix, the method comprising:

[0032] S1: Perform spectral transformation on the Hamiltonian matrix H to obtain the transformed matrix H';

[0033] S2: According to the matrix H', iteratively solve through the preset convergence criterion to obtain the eigenfunction;

[0034] S3: Ad...

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Abstract

The invention discloses a method and system for accurately and effectively solving the eigenstate of a large sparse matrix. The method comprises the steps: firstly enabling an original matrix H to beconverted into H' in a mode of spectral transformation, carrying out the psi'through an eigenfunction psi, and precisely giving the eigenvalue and the eigenfunction of the original matrix H through the quick solving of the psi'. According to the method, the solving of the eigenstate is an iterative solving process; according to the method, after an initial parameter is given, self-adjustment is carried out for iterative solving, on one hand, the dependence of the solving process on the initial value is reduced, on the other hand, the convergence rate is increased, the iterative solving efficiency of the matrix is greatly improved, universality is achieved for the bound state and the continuous state in the Hamiltonian quantity, and the method achieves the efficient and quick effects.

Description

technical field [0001] The invention relates to the technical field of engineering calculation, and more specifically relates to an accurate and effective method and system for solving the eigenstates of large sparse matrices. Background technique [0002] At present, most engineering and scientific research requires numerical calculation and solution, and the solution of many engineering and scientific problems often comes down to the solution of matrix in mathematical form, such as I 2 The solution process of molecular vibration and dissociation state, and this type of matrix is ​​sparse, large-dimensional, and eigenstates are difficult to solve effectively and accurately, especially the Hamiltonian sparse matrix. In the process of solving the matrix using existing methods , the dependence on the initial value is relatively large, and the convergence speed is slow, and the efficiency and accuracy of the solution process are difficult to guarantee. [0003] Therefore, how ...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/16
CPCG06F17/16
Inventor 林祥松沈建祥陈洪旭
Owner JIAXING UNIV
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