caa a22 4500 465751881 CHVBK 20180323111836.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF02242921 doi (NATIONALLICENCE)springer-10.1007/BF02242921 On the evaluation of one-dimensional Cauchy principal value integrals by rules based on cubic spline interpolation [Elektronische Daten] [Catterina Dagnino, Elisabetta Santi] Über die Berechnùng von eindimensionalen Integralen nach dem Hauptwert von Cauchy mittels Regeln auf der Basis kubischer Spline-Interpolation In this note we consider the numerical evaluation of one dimensional Cauchy principal value integrals of the form $$\rlap{--} \smallint _a^b \frac{{k(x)f(x)}}{{x - \lambda }}dx, a< \lambda< b,$$ 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≠C k [a, b],k=1, 2, 3 or 4. Some comparisons with other methods and numerical examples are also given. Springer-Verlag, 1990 Cauchy principla value integrals nationallicence cubic spline interpolation nationallicence product integration nationallicence Dagnino Catterina Facoltà di Ingegneria, Università di L'Aquila, I-67100, L'Aquila, Italy aut Santi Elisabetta Facoltà di Ingegneria, Università di L'Aquila, I-67100, L'Aquila, Italy aut Computing Springer-Verlag 43/3(1990-09-01), 267-276 0010-485X 43:3<267 1990 43 607 https://doi.org/10.1007/BF02242921 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02242921 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dagnino Catterina Facoltà di Ingegneria, Università di L'Aquila, I-67100, L'Aquila, Italy aut NATIONALLICENCE 700 1- Santi Elisabetta Facoltà di Ingegneria, Università di L'Aquila, I-67100, L'Aquila, Italy aut NATIONALLICENCE 773 0- Computing Springer-Verlag 43/3(1990-09-01), 267-276 0010-485X 43:3<267 1990 43 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer