Structure and approximation properties of Laplacian-like matrices
[EN] Many of today's problems require techniques that involve the solution of arbitrarily large systems Ax = b. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor decomposition. The numerical experiments support the fact that this al...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/212052 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/212052 |
| Access Level: | acceso abierto |
| Palabra clave: | Matrix decomposition Laplacian-like matrix High dimensional Linear System Matrix Lie Algebra Matrix Lie Group MATEMATICA APLICADA 04.- Garantizar una educación de calidad inclusiva y equitativa, y promover las oportunidades de aprendizaje permanente para todos |
| Sumario: | [EN] Many of today's problems require techniques that involve the solution of arbitrarily large systems Ax = b. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor decomposition. The numerical experiments support the fact that this algorithm converges especially fast when the matrix of the linear system is Laplacian-Like. These matrices that follow the tensor structure of the Laplacian operator are formed by sums of Kronecker product of matrices following a particular pattern. Moreover, this set of matrices is not only a linear subspace it is a Lie sub-algebra of a matrix Lie Algebra. In this paper, we characterize and give the main properties of this particular class of matrices. Moreover, the above results allow us to propose an algorithm to explicitly compute the orthogonal projection onto this subspace of a given square matrix A ¿ R^N×N . |
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