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An unusual way of solving linear systems

Gianfranco Cimmino (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Mediante integrali multipli agevoli per il calcolo numerico vengono espressi il valore assoluto di un determinante qualsiasi e le formule di Cramer.

Analytic interpolation and the degree constraint

Tryphon Georgiou (2001)

International Journal of Applied Mathematics and Computer Science

Analytic interpolation problems arise quite naturally in a variety of engineering applications. This is due to the fact that analyticity of a (transfer) function relates to the stability of a corresponding dynamical system, while positive realness and contractiveness relate to passivity. On the other hand, the degree of an interpolant relates to the dimension of the pertinent system, and this motivates our interest in constraining the degree of interpolants. The purpose of the present paper is to...

Anisotropic interpolation error estimates via orthogonal expansions

Mingxia Li, Shipeng Mao (2013)

Open Mathematics

We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.

Antiproximinal sets in the Banach space c ( X )

S. Cobzaş (1997)

Commentationes Mathematicae Universitatis Carolinae

If X is a Banach space then the Banach space c ( X ) of all X -valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C ( X ) V has a nearest point in V .

Application of Mazur-Orlicz's theorem in AMISE calculation

Karol Dziedziul (2002)

Applicationes Mathematicae

An approximation error and an asymptotic formula are given for shift invariant operators of polynomial order ϱ. Density estimators based on shift invariant operators are introduced and AMISE is calculated.

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