dorsal/arxiv
View SchemaModified conjugated gradient method for diagonalising large matrices
| Authors | Quanlin Jie, Dunhuan Liu |
|---|---|
| Categories | |
| ArXiv ID | physics/0309086 |
| URL | https://arxiv.org/abs/physics/0309086 |
| DOI | 10.1103/PhysRevE.68.056706 |
Abstract
We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trail vectors, play a similar role of the conjugated gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitably for first principle calculations.
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"date_created": "2026-03-02T18:00:46.556000Z",
"date_modified": "2026-03-02T18:00:46.556000Z",
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"abstract": "We present an iterative method to diagonalise large matrices. The basic idea\nis the same as the conjugated gradient (CG) method, i.e, minimizing the\nRayleigh quotient via its gradient and avoiding reintroduce errors to the\ndirections of previous gradients. Each iteration step is to find lowest\neigenvector of the matrix in a subspace spanned by the current trial vector and\nthe corresponding gradient of the Rayleigh quotient, as well as some previous\ntrial vectors. The gradient, together with the previous trail vectors, play a\nsimilar role of the conjugated gradient of the original CG algorithm. Our\nnumeric tests indicate that this method converges significantly faster than the\noriginal CG method. And the computational cost of one iteration step is about\nthe same as the original CG method. It is suitably for first principle\ncalculations.",
"arxiv_id": "physics/0309086",
"authors": [
"Quanlin Jie",
"Dunhuan Liu"
],
"categories": [
"physics.comp-ph",
"physics.chem-ph"
],
"doi": "10.1103/PhysRevE.68.056706",
"title": "Modified conjugated gradient method for diagonalising large matrices",
"url": "https://arxiv.org/abs/physics/0309086"
},
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