Best error bounds for quartic spline interpolation

Howell, Gary W.; Varma, A. K.

doi:10.1016/0021-9045(89)90008-7

Cited by 16 publications

(22 citation statements)

References 5 publications

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“…This study is organized as follows: First consider the spline function of degree six is presented which interpolates the lacunary data (0, 3,5). Some theoretical results about existence and uniqueness of the spline function of degree six are introduced and also convergence analysis is studied.…”

Section: Introductionmentioning

confidence: 99%

The Existence, Uniqueness and Error Bounds of Approximation Splines Interpolation for Solving Second-Order Initial Value Problems

Mm¹

2009

Journal of Mathematics and Statistics

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Problem statement: The lacunary interpolation problem, which we had investigated in this study, consisted in finding the six degree spline S(x) of deficiency four, interpolating data given on the function value and third and fifth order in the interval [0,1]. Also, an extra initial condition was prescribed on the first derivative. Other purpose of this construction was to solve the second order differential equations by two examples showed that the spline function being interpolated very well. The convergence analysis and the stability of the approximation solution were investigated and compared with the exact solution to demonstrate the prescribed lacunary spline (0, 3, 5) function interpolation. Approach: An approximation solution with spline interpolation functions of degree six and deficiency four was derived for solving initial value problems, with prescribed nonlinear endpoint conditions. Under suitable assumptions, the existences; uniqueness and the error bounds of the spline (0, 3, 5) function had been investigated; also the upper bounds of errors were obtained. Results: Numerical examples, showed that the presented spline function proved their effectiveness in solving the second order initial value problems. Also, we noted that, the better error bounds were obtained for a small step size h. Conclusion: In this study we treated for a first time a lacunary data (0,3,5) by constructing spline function of degree six which interpolated the lacunary data (0,3,5) and the constructed spline function applied to solve the second order initial value problems.

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Section: Introductionmentioning

confidence: 99%

The Existence, Uniqueness and Error Bounds of Approximation Splines Interpolation for Solving Second-Order Initial Value Problems

Mm¹

2009

Journal of Mathematics and Statistics

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“…The techniques used in proofs of Theorems 2, 2t, 3 and 31 are similar to those used by Hall and Meyer [1976] to give optimal bounds for derivatives of cubic spline and in previous joint work with A. K. Varma [1989].…”

Section: Concerning the Quartic S(x) We Can Showmentioning

confidence: 99%

Error bounds for two even degree tridiagonal splines

Howell

1990

International Journal of Stochastic Analysis

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“…This type of problem arises in the mathematical modeling of inhomogeneous lacunary interpolations concerning [1,4,10,11]. Spline function have been used for this purpose in minimize errors estimation [3,5,6]. Various types of splines, such as quadratic [2], quinitics [8],sixth [7] and ninth [9] have been used to interpolate the polynomial and solve these different kinds of problems.…”

Section: Introductionmentioning

confidence: 99%