The Experts below are selected from a list of 216 Experts worldwide ranked by ideXlab platform
E. Santi - One of the best experts on this subject based on the ideXlab platform.
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Uniform convergence results for certain two-dimensional Cauchy Principal Value integrals
2015Co-Authors: E. SantiAbstract:Abstract: A general uniform convergence theorem for numerical integration of certain two-dimensional Cauchy Principal Value integrals is proved. A special instance of this theorem is given as corollary.
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Convergence of rules based on nodal splines for the numerical evaluation of certain 2D Cauchy Principal Value integrals
Journal of Computational and Applied Mathematics, 1998Co-Authors: Catterina Dagnino, S. Perotto, E. SantiAbstract:Abstract We consider interpolatory type integration rules for the numerical approximation of certain 2D Cauchy Principal Value integrals, based on tensor product of nodal splines. We present convergence results which generalize those known in one-dimensional case.
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On the evaluation of Cauchy Principal Value integrals by rules based on quasi-interpolating splines
Journal of Computational and Applied Mathematics, 1996Co-Authors: E. SantiAbstract:Abstract In this paper we consider the numerical evaluation of one-dimensional Cauchy Principal Value integrals of the form ∫ −1 1 k(x) f(x) x−λ d x,−1 by rules obtained by subtracting out the singularity and then applying quadrature formulas based on quasi-interpolating splines.
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On the convergence of Turán type rules for Cauchy Principal Value integrals
CALCOLO, 1991Co-Authors: L. Gori Nicolò-amati, E. SantiAbstract:Some rules, based on Turán quadrature formulas, are derived for the numerical evaluation of one-dimensional Cauchy Principal Value integrals, and theorems on the convergence of a sequence of such rules are given.
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On the convergence of spline product quadratures for Cauchy Principal Value integrals
Journal of Computational and Applied Mathematics, 1991Co-Authors: Catterina Dagnino, E. SantiAbstract:Abstract In a recent paper (this journal (1990)), the authors proposed product integration formulas, for the numerical evaluation of the Cauchy Principal Value integral f1−1u(x) f;(x)/(x−λ) dx, based on cubic spline interpolation of f;, and obtained convergence results for functions f; ϵ Ck[−1, 1], k = 1, 2 or 3. In this report, the same rules are considered and their convergence is investigated for a larger class of functions f;. An error bound and some uniform convergence results are established, in the case of equally spaced quadrature nodes, for functions f;, satisfying a Holder condition of order μ on [−1, 1], 0
Kai Diethelm - One of the best experts on this subject based on the ideXlab platform.
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Interpolatory product quadratures for Cauchy Principal Value integrals with Freud weights
Numerische Mathematik, 1999Co-Authors: Steven B. Damelin, Kai DiethelmAbstract:We prove convergence results and error estimates for interpolatory product quadrature formulas for Cauchy Principal Value integrals on the real line with Freud–type weight functions. The formulas are based on polynomial interpolation at the zeros of orthogonal polynomials associated with the weight function under consideration. As a by–product, we obtain new bounds for the derivative of the functions of the second kind for these weight functions.
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New error bounds for modified quadrature formulas for Cauchy Principal Value integrals
Journal of Computational and Applied Mathematics, 1997Co-Authors: Kai DiethelmAbstract:Abstract For the numerical approximation of Cauchy Principal Value integrals, we consider the so-called modified quadrature formulas, i.e. formulas obtained by first subtracting out the singularity and then applying a classical quadrature formula. We are interested in error bounds holding uniformly for all possible positions of the singular point. The standard error bounds are based on suprema of derivatives, but they often overestimate the true errors by a factor that grows with the number of nodes of the quadrature formula. We give new bounds involving the total variation Var - ( s ) and L P -norms t |- ( s ) t | p of some derivative of the integrand function. These bounds give additional possibilities for sharper estimations of the error.
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uniform convergence of optimal order quadrature rules for Cauchy Principal Value integrals
Journal of Computational and Applied Mathematics, 1994Co-Authors: Kai DiethelmAbstract:Abstract For the numerical evaluation of Cauchy Principal Value integrals of the form , λe(−1, 1), f e C s [− 1, 1], we consider a quadrature method based on spline interpolation of odd degree 2 k + 1, k ∈N 0 . We show that these rules converge uniformly for λ ∈ (− 1, 1). In particular, we calculate the exact order of magnitude of the error and show that it is equal to the order of the optimal remainder in the class of functions with bounded s th derivative if s e s;;2 k + 1, 2 k + 2};. Finally, we compare the rule to the well-known quadrature rule of Elliott and Paget which only converges pointwise.
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Uniform convergence of optimal order quadrature rules for Cauchy Principal Value integrals
Journal of Computational and Applied Mathematics, 1994Co-Authors: Kai DiethelmAbstract:AbstractFor the numerical evaluation of Cauchy Principal Value integrals of the form , λε(−1, 1), f εCs[− 1, 1], we consider a quadrature method based on spline interpolation of odd degree 2k + 1,k ∈N0. We show that these rules converge uniformly for λ ∈ (− 1, 1). In particular, we calculate the exact order of magnitude of the error and show that it is equal to the order of the optimal remainder in the class of functions with bounded sth derivative if s ε s;;2k + 1, 2k + 2};. Finally, we compare the rule to the well-known quadrature rule of Elliott and Paget which only converges pointwise
Catterina Dagnino - One of the best experts on this subject based on the ideXlab platform.
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A UNIFORM CONVERGENT SEQUENCE OF SPLINE QUADRATURES FOR Cauchy Principal Value INTEGRALS
2015Co-Authors: Catterina Dagnino, Vittoria Demichelis, Quaderno N, Quaderni ScientificiAbstract:We propose a new quadrature rule for Cauchy Principal Value integrals, based on quadratic spline quasi-interpolants, which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights is given. Some numerical results and comparisons with another spline method are presented. Pubblicato in formato elettronic
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Spline Quasi-Interpolants with Boundary Interpolation Properties for Cauchy Principal Value Integrals
2008Co-Authors: Catterina Dagnino, Vittoria DemichelisAbstract:We propose new quadrature rules for Cauchy Principal Value integrals based on quadratic spline quasi‐interpolants, which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights and some numerical results are given.
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Convergence of rules based on nodal splines for the numerical evaluation of certain 2D Cauchy Principal Value integrals
Journal of Computational and Applied Mathematics, 1998Co-Authors: Catterina Dagnino, S. Perotto, E. SantiAbstract:Abstract We consider interpolatory type integration rules for the numerical approximation of certain 2D Cauchy Principal Value integrals, based on tensor product of nodal splines. We present convergence results which generalize those known in one-dimensional case.
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Numerical evaluation of Cauchy Principal Value integrals based on local spline approximation operators
Journal of Computational and Applied Mathematics, 1996Co-Authors: Catterina Dagnino, Paola LambertiAbstract:Abstract In this paper a local spline approximation method, defined for any function ƒ ϵ L 1 [−1, 1] , is applied to evaluate Cauchy Principal Value integrals and convergence results with an error bound are established. Some comparisons with other methods and numerical examples are given.
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On the convergence of spline product quadratures for Cauchy Principal Value integrals
Journal of Computational and Applied Mathematics, 1991Co-Authors: Catterina Dagnino, E. SantiAbstract:Abstract In a recent paper (this journal (1990)), the authors proposed product integration formulas, for the numerical evaluation of the Cauchy Principal Value integral f1−1u(x) f;(x)/(x−λ) dx, based on cubic spline interpolation of f;, and obtained convergence results for functions f; ϵ Ck[−1, 1], k = 1, 2 or 3. In this report, the same rules are considered and their convergence is investigated for a larger class of functions f;. An error bound and some uniform convergence results are established, in the case of equally spaced quadrature nodes, for functions f;, satisfying a Holder condition of order μ on [−1, 1], 0
Vittoria Demichelis - One of the best experts on this subject based on the ideXlab platform.
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A UNIFORM CONVERGENT SEQUENCE OF SPLINE QUADRATURES FOR Cauchy Principal Value INTEGRALS
2015Co-Authors: Catterina Dagnino, Vittoria Demichelis, Quaderno N, Quaderni ScientificiAbstract:We propose a new quadrature rule for Cauchy Principal Value integrals, based on quadratic spline quasi-interpolants, which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights is given. Some numerical results and comparisons with another spline method are presented. Pubblicato in formato elettronic
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Spline Quasi-Interpolants with Boundary Interpolation Properties for Cauchy Principal Value Integrals
2008Co-Authors: Catterina Dagnino, Vittoria DemichelisAbstract:We propose new quadrature rules for Cauchy Principal Value integrals based on quadratic spline quasi‐interpolants, which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights and some numerical results are given.
N Mohankumar - One of the best experts on this subject based on the ideXlab platform.
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An error analysis of the Cauchy Principal Value integral evaluation by the IMT scheme
Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 1998Co-Authors: N Mohankumar, A NatarajanAbstract:We provide an error analysis for the Cauchy Principal Value integral evaluation by the IMT method for analytic functions. We get the discretization error E d in terms of a contour integral and we derive an asymptotic estimate for this error integral which shows that E d = O [(e -∝(π N /2) )/ N 3/4 ]. We give two numerical examples, where the asymptotically estimated errors are compared with known actual Values.
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a comparison of some quadrature methods for approximating Cauchy Principal Value integrals
Journal of Computational Physics, 1995Co-Authors: A Natarajan, N MohankumarAbstract:Cauchy Principal Value integrals are evaluated by the IMT quadrature scheme, which like the TANH quadrature scheme is essentially a trapezoidal scheme, after making a transformation of the variable of integration. Numerical results for some test problems demonstrate that the IMT scheme is superior to the TANH scheme, while both these methods are comparable to, or even better than, the standard methods like the Gaussian or the Chebyshev schemes, in terms of accuracy and simplicity.