A Review of the Methods of Numerical Mathematics

Marchuk, G. I.

doi:10.1007/978-1-4615-9988-3_8

Cited by 6 publications

(3 citation statements)

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“…We have obtained the following estimate IW Eu*11 ak+1 Ilu*11~Ak+1' (19) m'n where u* is the normal solution, UC is the extrapolated solution by k: + 1 solutions of (18), Arnin is the smallest eigenvalue of A. From this estimate we establish that if applying the simple iterative method [22,27] to (18) then for achieving the normal solution of [La] with the given accuracy e by using the parametric extrapolation we reduce the computational amount G times in comparison with using only one shifted equation 18,…”

Section: Case 3 Ifmentioning

confidence: 89%

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Parametric extrapolation as a parallel method in mathematical physics.

Á¹

2012

JCC

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In recent years we have developed a parallel method for mathematical physics problems. It is the method of parametric extrapolation. In this paper we give an overview of our results concern ing this method for constructing parallel algorithms for some problems of mathematical physics. Torn tlit. Trong n h iing n arn gan day ch ung toi d a ph at trie'n mot ph u'o'ng ph ap song song gili mot so bai torin bien cii a v at Iy-toano Do la ph tro'rig ph ap ngoai suy theo t ham so. Bai b ao nay Ii tc!ng qu an c ac ket quti nghien ctru cii a chung toi lien quan den ph u'o'ng ph ap nay de' xfiy du'ng c ac th ufit toan song song giai mot so bai to.in bien cho ph trong trlnh elliptic cap hai v a cap bon o• rnu'c vi phfm cling nh ir o• rmrc roi r ac. Dordrecht-Kluwer Acad. Publ., 1995. [29) Zhu Jialin, Domain decomposition methods with boundary elements, In book: Boundary Element Methods, Proc. of the Fifth Japan-China Symposium on Boundary Element Methods,

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Section: Case 3 Ifmentioning

confidence: 89%

“…There are a lot of works concerning this problem (see e.g. monographs [22,27] and references therein).…”

Section: Accelerating the Convergence Rate Of Iterative Methods For Smentioning

confidence: 99%

Parametric extrapolation as a parallel method in mathematical physics.

Á¹

2012

JCC

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“…The matrices  and  correspond to the CC scheme and to the quadrature rule, respectively. The time integration of (44) is carried out with the combination of the Strang-Marchuk (SM) splitting scheme [37] [38] together with a predictor-corrector scheme [39]. We refer to [40] for a detailed introduction to splitting methods.…”

Section: Numerical Approximation Of the Optimality Systemsmentioning

confidence: 99%

On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

Gaviraghi¹,

Schindele²,

Annunziato³

et al. 2016

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A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework

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Lecture 19

Тыртышников

1997

A Brief Introduction to Numerical Analysis

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A Review of the Methods of Numerical Mathematics

Cited by 6 publications

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Parametric extrapolation as a parallel method in mathematical physics.

Parametric extrapolation as a parallel method in mathematical physics.

On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

Lecture 19

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