Abstract
Problem statement: Spline functions are the best tool of polynomials used as the basic means of approximation theory in nearly all areas of numerical analysis. Also in the problem of interpolation by g-spline construction of spline, existences, uniqueness and error bounds needed. Approach: In this study, we generalized (0,4) lacunary interpolation by quanta spline function. Results: The results obtained, the existence uniqueness and error bounds for generalize (0, 4) lacunary interpolation by qunatic spline. Conclusion: These generalize are preferable to interpolation by quantic spline to the use (0,4).
Highlights
Spline functions are the best tool of polynomials used as the basic means of approximation theory in most areas of numerical analysis
In this study we studied the generalization of one type of lacunary interpolation by quautic spline this type is (0,4) but in works (Varma, 1978; Venturino, 1996) showed this type but not in general
The lacunary interpolation problem, which we have investigated in this study, consists in finding the five degree spline S(x), interpolating data given on the function value and fourth order in the interval [0,1]
Summary
Spline functions are the best tool of polynomials used as the basic means of approximation theory in most areas of numerical analysis. During the past twentieth both the theories of splines and experiences with their use in numerical analysis have under gone a considerable degree of development. The following works deal to various degree with the theory and application of splines, (Ahlberg et al, 1967).
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