ON THE UNIFORM-CONVERGENCE OF CAUCHY PRINCIPAL VALUES OF QUASI-INTERPOLATING SPLINES

被引:9
|
作者
RABINOWITZ, P
SANTI, E
机构
[1] WEIZMANN INST SCI,DEPT APPL MATH & COMP SCI,IL-76100 REHOVOT,ISRAEL
[2] UNIV LAQUILA,DEPT ENERGET,I-67100 LAQUILA,ITALY
来源
BIT | 1995年 / 35卷 / 02期
关键词
CAUCHY PRINCIPAL VALUE; SPLINE;
D O I
10.1007/BF01737167
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
In this paper, quasi-interpolating splines are used to approximate the Cauchy principal value integral J(w(alpha beta)f;lambda) := integral(-1)(1) w(alpha beta)(x)f(x)/x-lambda dx, lambda is an element of (-1,1) where w(alpha beta)(x) := (1 - x)(alpha)(1 + x)(beta), alpha,beta > -1. We prove uniform convergence for the quadrature rules proposed here and give an algorithm for the numerical evaluation of these rules.
引用
收藏
页码:277 / 290
页数:14
相关论文
共 29 条
  • [11] Shape-preserving quasi-interpolating univariate cubic splines
    Conti, C
    Morandi, R
    Rabut, C
    MATHEMATICAL METHODS FOR CURVES AND SURFACES II, 1998, : 55 - 62
  • [12] UNIFORM-CONVERGENCE OF INTERPOLATION BY CUBIC-SPLINES
    GFRERER, H
    COMPUTING, 1982, 29 (04) : 361 - 364
  • [13] UNIFORM-CONVERGENCE OF OPTIMAL ORDER QUADRATURE-RULES FOR CAUCHY PRINCIPAL VALUE INTEGRALS
    DIETHELM, K
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1994, 56 (03) : 321 - 329
  • [15] A class of C2 quasi-interpolating splines free of Gibbs phenomenon
    Sergio Amat
    David Levin
    Juan Ruiz-Álvarez
    Juan C. Trillo
    Dionisio F. Yáñez
    Numerical Algorithms, 2022, 91 : 51 - 79
  • [16] A class of C2 quasi-interpolating splines free of Gibbs phenomenon
    Amat, Sergio
    Levin, David
    Ruiz-Alvarez, Juan
    Trillo, Juan C.
    Yanez, Dionisio F.
    NUMERICAL ALGORITHMS, 2022, 91 (01) : 51 - 79
  • [17] On C2 cubic quasi-interpolating splines and their computation by subdivision via blossoming
    Barrera, D.
    Eddargani, S.
    Lamnii, A.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 420
  • [18] Non-uniform WENO-based quasi-interpolating splines from the Bernstein-Bézier representation and applications
    Arandiga, F.
    Barrera, D.
    Eddargani, S.
    Ibanez, M. J.
    Roldan, J. B.
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 163 : 158 - 170
  • [19] FINITE PART INTEGRALS OF LOCAL BIVARIATE C1 QUASI-INTERPOLATING SPLINES
    C. Dagnino and P. Lambertri (Universita di Torino
    ApproximationTheoryandItsApplications, 2000, (04) : 68 - 79
  • [20] ON CONVERGENCE AND QUASI-REGULARITY OF INTERPOLATING COMPLEX PLANAR SPLINES
    OPFER, G
    SCHOBER, G
    MATHEMATISCHE ZEITSCHRIFT, 1982, 180 (04) : 469 - 481