A diagonal preconditioner for singularly perturbed problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F17%3A00005087" target="_blank" >RIV/46747885:24510/17:00005087 - isvavai.cz</a>
Result on the web
<a href="https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-017-0754-4" target="_blank" >https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-017-0754-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1186/s13661-017-0754-4" target="_blank" >10.1186/s13661-017-0754-4</a>

Result language
angličtina
Original language name
A diagonal preconditioner for singularly perturbed problems
Original language description
Using wavelet discretization with a standard wavelet diagonal preconditioning for singularly perturbed two-point boundary value problems, one can observe that condition numbers of arising stiffness matrices are growing with decreasing parameter &straightepsilon; when a nonsymmetric part starts to dominate. We propose here a simple diagonal preconditioning which significantly improves condition numbers of the stiffness matrices with a dominating nonsymmetric part and compare it with a standard wavelet preconditioning. Further, we prove that the condition numbers of diagonally preconditioned stiffness matrices are bounded independent of the matrix size. Numerical examples are given.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA16-09541S" target="_blank" >GA16-09541S: Robust numerical schemes for pricing of selected options under various market conditions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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