The Gauss quadrature for general linear functionals, Lanczos algorithm, and minimal partial realization
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438325" target="_blank" >RIV/00216208:11320/21:10438325 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=tU3ogcTO0f" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=tU3ogcTO0f</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-020-01052-y" target="_blank" >10.1007/s11075-020-01052-y</a>
Alternative languages
Result language
angličtina
Original language name
The Gauss quadrature for general linear functionals, Lanczos algorithm, and minimal partial realization
Original language description
The concept of Gauss quadrature can be generalized to approximate linear functionals with complex moments. Following the existing literature, this survey will revisit such generalization. It is well known that the (classical) Gauss quadrature for positive definite linear functionals is connected with orthogonal polynomials, and with the (Hermitian) Lanczos algorithm. Analogously, the Gauss quadrature for linear functionals is connected with formal orthogonal polynomials, and with the non-Hermitian Lanczos algorithm with look-ahead strategy; moreover, it is related to the minimal partial realization problem. We will review these connections pointing out the relationships between several results established independently in related contexts. Original proofs of the Mismatch Theorem and of the Matching Moment Property are given by using the properties of formal orthogonal polynomials and the Gauss quadrature for linear functionals.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Algorithms
ISSN
1017-1398
e-ISSN
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Volume of the periodical
88
Issue of the periodical within the volume
Říjen
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
32
Pages from-to
647-678
UT code for WoS article
000607330500001
EID of the result in the Scopus database
2-s2.0-85099372864