Lanczos algorithm and the complex Gauss quadrature
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10360929" target="_blank" >RIV/00216208:11320/18:10360929 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1553/etna_vol50s1" target="_blank" >https://doi.org/10.1553/etna_vol50s1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1553/etna_vol50s1" target="_blank" >10.1553/etna_vol50s1</a>
Alternative languages
Result language
angličtina
Original language name
Lanczos algorithm and the complex Gauss quadrature
Original language description
Gauss quadrature can be naturally generalized in order to approximate quasi-definite linear functionals, where the interconnections with (formal) orthogonal polynomials, (complex) Jacobi matrices, and the Lanczos algorithm are analogous to those in the positive definite case. In this survey we review these relationships with giving references to the literature that presents them in several related contexts. In particular, the existence of the n-weight (complex) Gauss quadrature corresponds to successfully performing the first n steps of the Lanczos algorithm for generating biorthogonal bases of the two associated Krylov subspaces. The Jordan decomposition of the (complex) Jacobi matrix can be explicitly expressed in terms of the Gauss quadrature nodes and weights and the associated orthogonal polynomials. Since the output of the Lanczos algorithm can be made real whenever the input is real, the value of the Gauss quadrature is a real number whenever all relevant moments of the quasi-definite linear functional are real.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamical and mathematical analysis of flows of complex fluids</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Transactions on Numerical Analysis
ISSN
1068-9613
e-ISSN
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Volume of the periodical
50
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
1-19
UT code for WoS article
000459296200002
EID of the result in the Scopus database
2-s2.0-85058210084