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Métodos para la actualización de los factores de Q y R de una matriz.

Laureano F. Escudero (1984)

Trabajos de Estadística e Investigación Operativa

Recientemente se han propuesto varios métodos para modificar los factores Q y R de una matriz una vez que se ha eliminado (o añadido) una fila o una columna. Normalmente la descripción de estos métodos se efectúa en el contexto de una determinada aplicación; quizá sea ésta la causa de su escasa difusión.

Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case

Jean Luc Guermond, Peter D. Minev (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.

Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case

Jean Luc Guermond, Peter D. Minev (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.

Mixed precision GMRES-based iterative refinement with recycling

Oktay, Eda, Carson, Erin (2023)

Programs and Algorithms of Numerical Mathematics

With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems A x = b have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential invocations,...

Model analysis of BPX preconditioner based on smoothed aggregation

Pavla Fraňková, Jan Mandel, Petr Vaněk (2015)

Applications of Mathematics

We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.

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