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Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space. / Gavurin, M. K.; Ryabov, V. M.

In: USSR Computational Mathematics and Mathematical Physics, Vol. 13, No. 6, 01.01.1973, p. 283-287.

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

Harvard

Gavurin, MK & Ryabov, VM 1973, 'Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space', USSR Computational Mathematics and Mathematical Physics, vol. 13, no. 6, pp. 283-287. https://doi.org/10.1016/0041-5553(73)90024-4

APA

Gavurin, M. K., & Ryabov, V. M. (1973). Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space. USSR Computational Mathematics and Mathematical Physics, 13(6), 283-287. https://doi.org/10.1016/0041-5553(73)90024-4

Vancouver

Gavurin MK, Ryabov VM. Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space. USSR Computational Mathematics and Mathematical Physics. 1973 Jan 1;13(6):283-287. https://doi.org/10.1016/0041-5553(73)90024-4

Author

Gavurin, M. K. ; Ryabov, V. M. / Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space. In: USSR Computational Mathematics and Mathematical Physics. 1973 ; Vol. 13, No. 6. pp. 283-287.

BibTeX

@article{5214baeb0d9c4e358fe814370e083a1c,
title = "Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space",
abstract = "WE consider in Hilbert space the equation Ax = f, where 0<A≤E, and only the approximation fδ of f, ∥fδ- f∥≤ δ. is known. We select a polynomial Pn (λ), which is expressed simply in terms of the Chebyshev polynomials Tn + in1 and approximates 1 λ, on [0, 1] fairly well, in the sense that the values of Pn(λ) are not too great on [0, ε] and are close to 1 λ, on [ε, 1], where ε is a small parameter. The approximate solution is represented in the form xδen = Pn(A)fδ. An estimate of the error is given.",
author = "Gavurin, {M. K.} and Ryabov, {V. M.}",
year = "1973",
month = jan,
day = "1",
doi = "10.1016/0041-5553(73)90024-4",
language = "English",
volume = "13",
pages = "283--287",
journal = "Computational Mathematics and Mathematical Physics",
issn = "0965-5425",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "6",

}

RIS

TY - JOUR

T1 - Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space

AU - Gavurin, M. K.

AU - Ryabov, V. M.

PY - 1973/1/1

Y1 - 1973/1/1

N2 - WE consider in Hilbert space the equation Ax = f, where 0<A≤E, and only the approximation fδ of f, ∥fδ- f∥≤ δ. is known. We select a polynomial Pn (λ), which is expressed simply in terms of the Chebyshev polynomials Tn + in1 and approximates 1 λ, on [0, 1] fairly well, in the sense that the values of Pn(λ) are not too great on [0, ε] and are close to 1 λ, on [ε, 1], where ε is a small parameter. The approximate solution is represented in the form xδen = Pn(A)fδ. An estimate of the error is given.

AB - WE consider in Hilbert space the equation Ax = f, where 0<A≤E, and only the approximation fδ of f, ∥fδ- f∥≤ δ. is known. We select a polynomial Pn (λ), which is expressed simply in terms of the Chebyshev polynomials Tn + in1 and approximates 1 λ, on [0, 1] fairly well, in the sense that the values of Pn(λ) are not too great on [0, ε] and are close to 1 λ, on [ε, 1], where ε is a small parameter. The approximate solution is represented in the form xδen = Pn(A)fδ. An estimate of the error is given.

UR - http://www.scopus.com/inward/record.url?scp=49349138890&partnerID=8YFLogxK

U2 - 10.1016/0041-5553(73)90024-4

DO - 10.1016/0041-5553(73)90024-4

M3 - Article

AN - SCOPUS:49349138890

VL - 13

SP - 283

EP - 287

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 6

ER -

ID: 35464236