On multivariate polynomials of least deviation from zero on the unit ball

Reimer, Manfred

doi:10.1007/bf01214733

Cited by 18 publications

(12 citation statements)

References 6 publications

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“…In [3], the function t~*t 4 was approximated on the unit circle by bivariate polynomials of total degree 7. From [12,18], the optimal error in (tl, t2) -=(cos ~b, sin 4)) is 2 -7 cos 8 q5 so that the same solution is obtained on a discrete set containing the extrema defined by q~ =jrc/8 (0 <j< 15). This occurs with m points equally spaced from 1 where m is a multiple of 16, which yields Ax ~ b with A e P," • 36 and b e R".…”

Section: -1mentioning

confidence: 97%

Strict Chebyshev approximation for general systems of linear equations

Thiran

Thiry

1987

Numer. Math.

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Summary. An ascent exchange algorithm for computing the strict Chebyshev solution to general systems of linear equations is presented. It uses generalized exchange rules to ensure convergence and splits up the entire system into subsystems by means of a canonical decomposition of a matrix obtained by Gaussian elimination methods. All updating procedures are developed and several numerical examples illustrate the efficiency of the algorithm.

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Section: -1mentioning

confidence: 97%

Strict Chebyshev approximation for general systems of linear equations

Thiran

Thiry

1987

Numer. Math.

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“…The problem of high-dimension approximation has attracted a wide attention [13][14][15][16][17][18]. Here we will present a novel recursive method to approximate d-variate functions.…”

Section: The D-variate Functions On [ ] Dmentioning

confidence: 99%

A novel recursive method to reconstruct multivariate functions on the unit cube

Zhang

2017

Open Mathematics

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“…According to a result of Reimer [7] the polynomials A m are (for r=2) the polynomials of least deviation from zero with respect to the maximum norm, thus yielding that the Kergin interpolants to the equidistant nodes of Liang are best approximations to the monomials (see [5]). …”

Section: Identification Of Certain Polynomial Families As Kergin Remamentioning

confidence: 99%

On Best Approximation of the Monomials on the Unit Ball of Rr

Maier

1998

Journal of Approximation Theory

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Bos and Liang have separately proved that the Kergin interpolants with respect to distinguished nodes on the unit disk are best approximations of the monomials in the infinity norm. These results are extended by characterizing the nodes as solutions of a system of nonlinear equations. Thus, it is possible to get all nodes with this property on the unit disk and it is likewise possible to lift results to the ball in the sense of approximation in the mean.1998 Academic Press

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On multivariate polynomials of least deviation from zero on the unit ball

Cited by 18 publications

References 6 publications

Strict Chebyshev approximation for general systems of linear equations

Strict Chebyshev approximation for general systems of linear equations

A novel recursive method to reconstruct multivariate functions on the unit cube

On Best Approximation of the Monomials on the Unit Ball of Rr

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