Application of linear fractional transformation in problems of localization of matrix spectra and roots of polynomials

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Application of linear fractional transformation in problems of localization of matrix spectra and roots of polynomials. / Biberdorf, E. A.; Wang, L.

In: Siberian Electronic Mathematical Reports, Vol. 21, No. 2, 2024, p. B46-B63.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c2098d2cfe4a44499e7f755a6ea7414c,

title = "Application of linear fractional transformation in problems of localization of matrix spectra and roots of polynomials",

abstract = "The paper investigates the possibilities of using linear fractional transformations in a number of problems that can be reduced to spectral dichotomy. More specifically, for the dichotomy of the imaginary axis, estimates arc given for areas containing eigenvalues, methods for determining the absence of a matrix spectrum on a ray and a segment- arc described. A method for dividing a polynomial into two factors whose roots lie in the right and left half-planes is described and substantiated.",

keywords = "factorization of a polynomial, linear fractional transformation, spectrum dichotomy",

author = "Biberdorf, {E. A.} and L. Wang",

note = "This work was accomplished within the state assignment of the Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008.",

year = "2024",

doi = "10.33048/semi.2024.21.B04",

language = "English",

volume = "21",

pages = "B46--B63",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

number = "2",

}

RIS

TY - JOUR

T1 - Application of linear fractional transformation in problems of localization of matrix spectra and roots of polynomials

AU - Biberdorf, E. A.

AU - Wang, L.

N1 - This work was accomplished within the state assignment of the Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008.

PY - 2024

Y1 - 2024

N2 - The paper investigates the possibilities of using linear fractional transformations in a number of problems that can be reduced to spectral dichotomy. More specifically, for the dichotomy of the imaginary axis, estimates arc given for areas containing eigenvalues, methods for determining the absence of a matrix spectrum on a ray and a segment- arc described. A method for dividing a polynomial into two factors whose roots lie in the right and left half-planes is described and substantiated.

AB - The paper investigates the possibilities of using linear fractional transformations in a number of problems that can be reduced to spectral dichotomy. More specifically, for the dichotomy of the imaginary axis, estimates arc given for areas containing eigenvalues, methods for determining the absence of a matrix spectrum on a ray and a segment- arc described. A method for dividing a polynomial into two factors whose roots lie in the right and left half-planes is described and substantiated.

KW - factorization of a polynomial

KW - linear fractional transformation

KW - spectrum dichotomy

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85216960378&origin=inward&txGid=f89ff5d614406afb35bd440322219084

UR - https://www.mendeley.com/catalogue/7dee486a-6a75-3609-b4bb-a5c6cddf064d/

U2 - 10.33048/semi.2024.21.B04

DO - 10.33048/semi.2024.21.B04

M3 - Article

VL - 21

SP - B46-B63

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -

ID: 64619636