# An Interval Polynomial Interpolation Problem and Its Lagrange Solution

An Interval Polynomial Interpolation Problem and Its Lagrange Solution In many practical problems, we need to use interpolation: we know that the value of a quantity is uniquely determined by some other quantity x (i.e., y = f(x)), we have measured several pairs of values (xi, yi), and we want to predict y for a given x. We can only guarantee estimates for y if we have some a priori information about the function f(x). In particular, in some problems, we know that f(x) is a polynomial of known degree d (e.g., that it is linear, or that it is quadratic). For this polynomial interpolation, with interval uncertainty of the input data (xi, yi), we present several reasonable algorithms that compute, for a given x0, guaranteed bounds for f(x0). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# An Interval Polynomial Interpolation Problem and Its Lagrange Solution

, Volume 4 (1) – Oct 6, 2004
12 pages

/lp/springer_journal/an-interval-polynomial-interpolation-problem-and-its-lagrange-solution-mGqqg3wECk
Publisher
Springer Journals
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009946531786
Publisher site
See Article on Publisher Site

### Abstract

In many practical problems, we need to use interpolation: we know that the value of a quantity is uniquely determined by some other quantity x (i.e., y = f(x)), we have measured several pairs of values (xi, yi), and we want to predict y for a given x. We can only guarantee estimates for y if we have some a priori information about the function f(x). In particular, in some problems, we know that f(x) is a polynomial of known degree d (e.g., that it is linear, or that it is quadratic). For this polynomial interpolation, with interval uncertainty of the input data (xi, yi), we present several reasonable algorithms that compute, for a given x0, guaranteed bounds for f(x0).

### Journal

Reliable ComputingSpringer Journals

Published: Oct 6, 2004

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