- Volume 58 Issue 3
In this paper, we present a symbolic formulation of the error obtained due to an approximation of a given function by the mixed-interpolating function. Using the proposed symbolic method, we compute the error evaluation operator as well as the error estimation at any arbitrary point. We also present an algorithm to compute an approximation of a function by the mixed interpolation technique in terms of projector operator. Certain examples are presented to illustrate the proposed algorithm. Maple implementation of the proposed algorithm is discussed with sample computations.
mixed interpolation;error estimation;projector;Stieltjes functionals;symbolic method
- A. Chakrabarti and Hamsapriye, Derivation of a general mixed interpolation formula, J. Comput. Appl. Math., 70(1996), 161-172.
- J. P. Coleman, Mixed interpolation methods with arbitrary nodes, J. Comput. Appl. Math., 92(1998), 69-83.
- P. J. Davis, Interpolation and Approximation, Blaisdell Publishing Co., New York-Toronto-London, 1963.
- H. W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers Group, Dordrecht, 1996.
- A. Korporal, G. Regensburger and M. Rosenkranz, A Maple package for integrodi fferential operators and boundary problems, ACM Communications in Computer Algebra, 44(3)(2010), 120-122.
- H. D. Meyer, J. Vanthournout and G. V. Berghe, On a new type of mixed interpolation, J. Comput. Appl. Math., 30(1)(1990), 55-69. https://doi.org/10.1016/0377-0427(90)90005-K
- H. D. Meyer, J. Vanthournout, G. V. Berghe and A. Vanderbauwhede, On the error estimation for a mixed type of interpolation, J. Comput. Appl. Math., 32(1990), 407-415. https://doi.org/10.1016/0377-0427(90)90045-2
- R. Piziak and P. L. Odell, Matrix Theory: From Generalized Inverse to Jordan Form, Chapman & Hall/CRC, Boca Raton, FL, 2007.
- M. Rosenkranz, G. Regensburger, L. Tec, and B. Buchberger, Symbolic analysis for boundary problems: from rewriting to parametrized Groner bases, Texts Monogr. Symbol. Comput., SpringerWienNewYork, Vienna, 2012.
- S. Thota and S. D. Kumar, Symbolic method for polynomial interpolation with stieltjes conditions, Proceedings of International Conference on Frontiers in Mathematics 2015, 225-228.
- S. Thota and S. D. Kumar, On a mixed interpolation with integral conditions at arbitrary nodes, Cogent Math., 3(2016), Art. ID 1151613, 10 pp.
- S. Thota and S. D. Kumar, Symbolic algorithm for a system of differential-algebraic equations, Kyungpook Math. J., 56(4)(2016), 1141-1160. https://doi.org/10.5666/KMJ.2016.56.4.1141
- S. Thota and S. D. Kumar, Solving system of higher-order linear differential equations on the level of operators, Int. J. Pure Appl. Math., 106(1)(2016), 11-21.