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Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems

H. Saberi Najafi, S. A. Edalatpanah (2013)

RAIRO - Operations Research - Recherche Opérationnelle

For solving linear complementarity problems LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting. But up to now, no paper has discussed the effect of preconditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and we use a class of preconditioners with generalized Accelerated Overrelaxation (GAOR) methods and analyze the convergence of these methods for LCP. Furthermore, Comparison between our methods...

Lanczos-like algorithm for the time-ordered exponential: The * -inverse problem

Pierre-Louis Giscard, Stefano Pozza (2020)

Applications of Mathematics

The time-ordered exponential of a time-dependent matrix 𝖠 ( t ) is defined as the function of 𝖠 ( t ) that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in 𝖠 ( t ) . The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to a non-commutative convolution-like product, denoted by * . Yet, the existence of such inverses, crucial to...

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution

Kamyar Malakpoor, Enrique F. Kaasschieter, Jacques M. Huyghe (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci.35 (1997) 793–802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part I: Modeling of incompressible charged porous media. ESAIM: M2AN41 (2007) 661–678]. This theory results in a coupled system of nonlinear parabolic differential equations together with an algebraic...

Metoda konjugovaných gradientů jako dobrodružství jdoucí přes staletí

Zdeněk Strakoš (2020)

Pokroky matematiky, fyziky a astronomie

Metoda konjugovaných gradientů a Lanczosova metoda tvoří historický a metodologický základ tzv. metod krylovovských podprostorů pro numerickou aproximaci řešení lineárních rovnic a částečnou aproximaci spektra lineárních operátorů. Ačkoliv jsou v obecném povědomí spojovány především s numerickým řešením velmi rozsáhlých soustav lineárních algebraických rovnic a aproximací vlastních čísel velkých matic, je přirozené uvažovat jejich formulaci v kontextu operátorů na Hilbertových prostorech (konečné...

Currently displaying 241 – 260 of 549