### 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 language | English |
---|---|

Pages (from-to) | 340-351 |

Number of pages | 12 |

Journal | WSEAS Transactions on Mathematics |

Volume | 17 |

Publication status | Published - 1 Jan 2018 |

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### 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

*WSEAS Transactions on Mathematics*,

*17*, 340-351.

}

*WSEAS Transactions on Mathematics*, vol. 17, pp. 340-351.

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

Research output

TY - JOUR

T1 - About adaptive grids construction

AU - Burova, I. G.

AU - Muzafarova, E. F.

AU - Zhilin, D. E.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

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.

KW - Adaptive grid of nodes

KW - Approximation

KW - Non-polynomial splines

KW - polynomial splines

KW - Tensor product

UR - http://www.scopus.com/inward/record.url?scp=85060587636&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85060587636

VL - 17

SP - 340

EP - 351

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -