Journal Article10.1007/BF02252079
Some algorithms for interval interpolating polynomial
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TL;DR: Some algorithms for the computation of an Interval Interpolating Polynomial have been proposed and one of the algorithms has been shown to be superior to all others.
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Abstract: Some algorithms for the computation of an Interval Interpolating Polynomial have been proposed. The algorithms have been compared with the existing algorithms. One of the algorithms has been shown to be superior to all others.
read more
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Citations
Optimal approximations in interval analysis
Helmut Ratschek
- 01 Jan 1980
TL;DR: In this paper, an interval analytic approximation theory is presented and a comparison of two kinds of approximations are made: the first one is transferred from approximation theory of linear spaces using only terms of order theory and no terms of topology or functional analysis, and the second one arises from the aim that an approximation should not only be seen as any operator that assigns a function to a function by any less or more abstract manner but also submit an effective procedure or algorithm how to compute assignments.
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On the computation of Hermite interval interpolating polynomials
TL;DR: Two algorithms for the computation of Hermite interval interpolating polynomial have been proposed, one of which is recommended for fast computation and the other for obtaining the most accurate results.
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Multivariate interval interpolation
G.P. Bhattacharjee,K.L. Majumder +1 more
TL;DR: Two algorithms for the computation of a multivariate interval interpolating polynomial have been proposed and the algorithms have been compared among themselves with respect to the number of interval arithmetic operations required to compute them and the width of the computed intervals.
1
The iterative solution of initial value problems for ordinary differential equations
TL;DR: Newton's interval method for solving a problem with an interval specification of the initial data for differential equations is discussed in this paper, where the results of some previous papers of the author are generalized.
References
On the Newton Method in Interval Analysis
Karl Nickel
- 01 Dec 1971
TL;DR: In this paper, an interval type Newton method for vector equations in the n-dimensional Euclidean space is investigated, where the interval is defined as the interval of the interval.
72
Quadratic convergence in interval arithmetic, part II
William Chuba,Webb Miller +1 more
TL;DR: In this paper, the authors investigated the effect of dependence on the error of one operation in an interval arithmetic procedure and proved the quadratic convergence of the "centered form" and of a method of Hansen and Smith for solving linear algebraic systems.
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More on quadratic convergence in interval arithmetic
TL;DR: In this article, necessary and sufficient conditions for "quadratic convergence" in interval arithmetic are given for interval arithmetic with quadratic convergence. But these conditions are not applicable to interval arithmetic without interval arithmetic.
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