TITLE

Monotone and convex interpolation by weighted cubic splines

AUTHOR(S)
Kvasov, B.
PUB. DATE
October 2013
SOURCE
Computational Mathematics & Mathematical Physics;Oct2013, Vol. 53 Issue 10, p1428
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Algorithms for interpolating by weighted cubic splines are constructed with the aim of preserving the monotonicity and convexity of the original discrete data. The analysis performed in this paper makes it possible to develop two algorithms with the automatic choice of the shape-controlling parameters (weights). One of them preserves the monotonicity of the data, while the other preserves the convexity. Certain numerical results are presented.
ACCESSION #
91552255

 

Related Articles

  • A Nonmonotone Line Search Slackness Technique for Unconstrained Optimization. Hu, Ping; Liu, Xu-Qing // Journal of Optimization Theory & Applications;Sep2013, Vol. 158 Issue 3, p773 

    This paper mainly aims to study a new nonmonotone line search slackness technique for unconstrained optimization problems and show that it possesses the global convergence without needing condition of convexity. We establish the corresponding algorithm and illustrate its effectiveness by virtue...

  • Convexity preserving interpolation by splines of arbitrary degree. Verlan, Igor // Computer Science Journal of Moldova;2010, Vol. 18 Issue 1, p54 

    In the present paper an algorithm of C2 interpolation of discrete set of data is given using splines of arbitrary degree, which preserves the convexity of given set of data.

  • Monotone and convex interpolation by weighted quadratic splines. Kvasov, Boris // Advances in Computational Mathematics;Feb2014, Vol. 40 Issue 1, p91 

    In this paper we discuss the design of algorithms for interpolating discrete data by using weighted C quadratic splines in such a way that the monotonicity and convexity of the data are preserved. The analysis culminates in two algorithms with automatic selection of the shape control parameters:...

  • Accuracy Certificates for Computational Problems with Convex Structure. Nemirovski, Arkadi; Onn, Shmuel; Rothblum, Uriel G. // Mathematics of Operations Research;Feb2010, Vol. 35 Issue 1, p52 

    The goal of this paper is to introduce the notion of certificates, which verify the accuracy of solutions of computational problems with convex structure. Such problems include minimizing convex functions, variational inequalities with monotone operators, computing saddle points of...

  • Solving variational inequalities with monotone operators on domains given by Linear Minimization Oracles. Juditsky, Anatoli; Nemirovski, Arkadi // Mathematical Programming;Mar2016, Vol. 156 Issue 1/2, p221 

    The standard algorithms for solving large-scale convex-concave saddle point problems, or, more generally, variational inequalities with monotone operators, are proximal type algorithms which at every iteration need to compute a prox-mapping, that is, to minimize over problem's domain X the sum...

  • Iterative Schemes for Finite Families of Maximal Monotone Operators Based on Resolvents. Li Wei; Ruilin Tan // Abstract & Applied Analysis;2014, p1 

    The purpose of this paper is to present two iterative schemes based on the relative resolvent and the generalized resolvent, respectively. And, it is shown that the iterative schemes converge weakly to common solutions for two finite families of maximal monotone operators in a real smooth and...

  • Convexity of the Proximal Average. Johnstone, Jennifer A.; Koch, Valentin R.; Lucet, Yves // Journal of Optimization Theory & Applications;Jan2011, Vol. 148 Issue 1, p107 

    We complete the study of the convexity of the proximal average by proving it is convex as a function of each of its parameters separately, but not jointly convex as a function of any two of its parameters. We present an interpolation-based plotting algorithm that takes advantage of the partial...

  • Convexity Preserving Interpolation by GC²-Rational Cubic Spline. Dube, M.; Rana, P. S. // International Journal of Computer Applications;Dec2013, Vol. 84, p1 

    A weighted rational cubic spline interpolation has been constructed using rational spline with quadratic denominator. GC1-piecewise rational cubic spline function involving parameters has been constructed which produces a monotonic interpolant to given monotonic data . The degree of smoothness...

  • Use of B-spline curves and genetic algorithms to reduce the sidelobe level in array-patterns. Wen-Chia Lue; Fang Hsu // Microwave & Optical Technology Letters;8/20/2003, Vol. 38 Issue 4, p308 

    A method of minimizing the sidelobe level for linear array patterns by amplitude-only adjustment in element excitations, which involves combining B-spline techniques and genetic algorithms, is considered. We demonstrate this technique using a 30-element linear array. It is also capable of...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics