Abstract

One of the important tasks of interpolation is the good selection of interpolation nodes. As is well known, the roots of the Chebyshev polynomial are optimal ones for interpolation with algebraic polynomials on the interval [-1,1]. Nevertheless, there are still some difficulties in constructing the grid of nodes when the number of points tend to infinity. Here we offer the formula for constructing the interpolation nodes for a rapidly increasing function or decreasing function. The formula takes into account the local behavior of the function on the previous three grid nodes, and it is based on the interpolation by local quadratic polynomial splines. Particular attention is paid to the interpolation of functions on radial-ring grids.

Original languageEnglish
Pages (from-to)340-351
Number of pages12
JournalWSEAS Transactions on Mathematics
Volume17
Publication statusPublished - 1 Jan 2018

Fingerprint

Adaptive Grid
Interpolation
Interpolate
Polynomials
Vertex of a graph
Grid
Quadratic Spline
Local Polynomial
Polynomial Splines
Algebraic Polynomial
Quadratic Polynomial
Increasing Functions
Chebyshev Polynomials
Splines
Infinity
Roots
Tend
Ring
Interval
Node

Scopus subject areas

  • Algebra and Number Theory
  • Endocrinology, Diabetes and Metabolism
  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Management Science and Operations Research
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

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About adaptive grids construction. / Burova, I. G.; Muzafarova, E. F.; Zhilin, D. E.

In: WSEAS Transactions on Mathematics, Vol. 17, 01.01.2018, p. 340-351.

Research output

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AB - One of the important tasks of interpolation is the good selection of interpolation nodes. As is well known, the roots of the Chebyshev polynomial are optimal ones for interpolation with algebraic polynomials on the interval [-1,1]. Nevertheless, there are still some difficulties in constructing the grid of nodes when the number of points tend to infinity. Here we offer the formula for constructing the interpolation nodes for a rapidly increasing function or decreasing function. The formula takes into account the local behavior of the function on the previous three grid nodes, and it is based on the interpolation by local quadratic polynomial splines. Particular attention is paid to the interpolation of functions on radial-ring grids.

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