Elisabetta Santi

Numerical integration based on quasi-interpolating splines

In this paper product quadrature rules based on quasi-interpolating splines are proposed and convergence results are proved for bounded integrands. Convergence results are also proved for sequences of Cauchy principal value integrals of these quasiinterpolating splines. Some comparisons with other methods and numerical examples are given.ZusammenfassungDie vorliegende Arbeit behandelt auf quasiinterpolierenden Splines basierende Produktquadraturformeln und beweist Konvergenzresultate für limitierte Integranden. Konvergenzresultate mit diesen quasi-interpolierenden Splines werden auch für Cauchysche Hauptwertintegralsequenzen bewiesen. Vergleiche mit anderen Methoden und numerische Beispiele werden angegeben.

An algorithm for numerical integration based on quasi-interpolating splines

In this paper product quadratures based on quasi-interpolating splines are proposed for the numerical evaluation of integrals with anL1-kernel and of Cauchy Principal Value integrals.

On the evaluation of one-dimensional Cauchy principal value integrals by rules based on cubic spline interpolation

AbstractIn this note we consider the numerical evaluation of one dimensional Cauchy principal value integrals of the form

Local spline approximation methods for singular product integration

\rlap{--} \smallint _a^b \frac{{k(x)f(x)}}{{x - \lambda }}dx, a< \lambda< b,

Original article: Numerical evaluation of certain hypersingular integrals using refinable operators

by rules obtained by “subtracting out” the singularity and then applying product quadratures based on cubic spline interpolation at equally spaced nodes. Convergence results are established for Hölder continuous functions of order, μ, 0<μ≤1, and asymptotic rates are obtained for functionsf≠Ck[a, b],k=1, 2, 3 or 4. Some comparisons with other methods and numerical examples are also given.ZusammenfassungIn dieser Arbeit betrachten wir die numerische Bestimmung von eindimensionalen Integralen vom Cauchyschen Hauptwert vom Typ

On a class of shape-preserving refinable functions with dilation 3

\rlap{--} \smallint _a^b \frac{{k(x)f(x)}}{{x - \lambda }}dx, a< \lambda< b,