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

M. K. Gavurin, V. M. Ryabov

Результат исследований: Научные публикации в периодических изданияхстатья

3 Цитирования (Scopus)


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.

Язык оригиналаанглийский
Страницы (с-по)283-287
Число страниц5
ЖурналUSSR Computational Mathematics and Mathematical Physics
Номер выпуска6
СостояниеОпубликовано - 1 янв 1973