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 -