On the conditioning of the Newton formula for Lagrange interpolation

Lam, Dinh Huu; Cuong, Le Ngoc; Manh, Phung Van; Minh, Nguyễn Văn

doi:10.1016/j.jmaa.2021.125473

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Conditioning Of Least Squares Problems1

Introduction1

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2023

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Cited by 4 publications

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“…The integral defining h α j+m, j can be expressed in terms of the square of the norm of the usual Jacobi polynomials (see formula (8) of [6]) giving rise to…”

Section: Conditioning Of Least Squares Problemsmentioning

confidence: 99%

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On the stability of the representation of finite rank operators

2023

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The stability of the representation of finite rank operators in terms of a basis is analyzed. A conditioning is introduced as a measure of the stability properties. This conditioning improves some other conditionings because it is closer to the Lebesgue function. Improved bounds for the conditioning of the Fourier sums with respect to an orthogonal basis are obtained, in particular, for Legendre, Chebyshev, and disk polynomials. The Lagrange and Newton formulae for the interpolating polynomial are also considered.

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“…The integral defining h α j+m, j can be expressed in terms of the square of the norm of the usual Jacobi polynomials (see formula (8) of [6]) giving rise to…”

Section: Conditioning Of Least Squares Problemsmentioning

confidence: 99%

“…In previous research, a different conditioning for comparing different representations of an operator has been considered [3][4][5][6]8]. However, this conditioning tends to overestimate the instability, especially when dealing with Fourier representations with respect to orthogonal polynomials, as we shall see later.…”

Section: Introductionmentioning

confidence: 99%