Nodal splines on compact intervals

Siewer, Ralf

doi:10.1007/s10543-013-0429-1

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Martensen Splines2

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2014

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Cited by 1 publication

(2 citation statements)

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“…In this section, we give the necessary background material on Martensen splines as presented in [15,16,17] and [5].…”

Section: Martensen Splinesmentioning

confidence: 99%

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Martensen splines and finite-part integrals

Demichelis

Sciarra

2014

Numer Algor

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We state a uniform convergence theorem for finite-part integrals which are derivatives of weighted Cauchy principal value integrals. We prove that a sequence of Martensen splines, based on locally uniform meshes, satisfies the sufficient conditions required by the theorem. We construct the quadrature rules based on such splines and illustrate their behaviour by presenting some numerical results and comparisons with composite midpoint, Simpson and Newton-Cotes rules.

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“…In this section, we give the necessary background material on Martensen splines as presented in [15,16,17] and [5].…”

Section: Martensen Splinesmentioning

confidence: 99%

“…Assuming that f ∈ C n−1 ([a, b]), the defining formula for the Martensen spline M R ( f ) of degree n on [a, b] is given by [17],…”

Section: Martensen Splinesmentioning

confidence: 99%