DOI QR코드

DOI QR Code

POLYNOMIAL-FITTING INTERPOLATION RULES GENERATED BY A LINEAR FUNCTIONAL

Kim Kyung-Joong

  • Published : 2006.04.01

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

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
  3. L. Gr. Ixaru and B. Paternoster, A Gauss Quadrature Rule for Oscillatory Integrands, Comput. Phys, Comm. 133 (2001), 177-188 https://doi.org/10.1016/S0010-4655(00)00173-9
  4. 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 https://doi.org/10.1016/S0377-0427(00)00599-9
  5. 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 https://doi.org/10.1016/S0377-0427(01)00483-6
  6. V. I. Krylov, Approximate Calculation of Integrals, Macmillan, New York, 1962
  7. W. Rudin, Principles of Mathematical Analysis, McGRAW-Hill, Singapore, 1976
  8. 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 https://doi.org/10.1016/S0010-4655(02)00676-8
  9. 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 https://doi.org/10.1016/S0377-0427(01)00474-5
  10. K. J. Kim, Two-frequency-dependent Gauss quadrature rules, J. Comput. Appl. Math. 174 (2005), 43-55 https://doi.org/10.1016/j.cam.2004.03.020
  11. L. Gr. Ixaru, Operations on Oscillatory Functions, Comput. Phys. Comm. 105 (1997), 1-19 https://doi.org/10.1016/S0010-4655(97)00067-2