POLYNOMIAL-FITTING INTERPOLATION RULES GENERATED BY A LINEAR FUNCTIONAL

- Journal title : Communications of the Korean Mathematical Society
- Volume 21, Issue 2, 2006, pp.397-407
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2006.21.2.397

Title & Authors

POLYNOMIAL-FITTING INTERPOLATION RULES GENERATED BY A LINEAR FUNCTIONAL

Kim Kyung-Joong;

Kim Kyung-Joong;

Abstract

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f` at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

Keywords

Interpolation rule;Hermite polynomial;

Language

English

Cited by

References

1.

K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley and Sons, 1989

2.

R. L. Burden and J. D. Faires, Numerical Analysis, Brooks/Cole, 2001

4.

L. Gr. Ixaru and B. Paternoster, A Gauss Quadrature Rule for Oscillatory Integrands, Comput. Phys, Comm. 133 (2001), 177-188

5.

L. Gr. Ixaru, M. Rizea, H. De Meyer, G. Vanden Berghe, Weights of the exponential fitting multistep algorithms for first order ODEs, J. Comput. Appl. Math. 132 (2001), 83-93

6.

L. Gr. Ixaru, G. Vanden Berghe and M. De Meyer, Exponentially fitted variable two-step BDF algorithm for first order ODEs, Comput. Phys. Comm. 150 (2003), 116-128

7.

L. Gr. Ixaru, G. Vanden Berghe and M. De Meyer, Frequency evaluation in exponential fitting multistep algorithms for ODEs, J. Comput. Appl. Math. 140 (2002), 423-434

8.

9.

K. J. Kim, R. Cools and L. Gr. Ixaru, Quadrature rules using first derivatives for oscillatory integrands, J. Comput. Appl. Math. 140 (2002), 479-497

10.

V. I. Krylov, Approximate Calculation of Integrals, Macmillan, New York, 1962

11.

W. Rudin, Principles of Mathematical Analysis, McGRAW-Hill, Singapore, 1976