Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes

Alfredo Eisinberg; Giuseppe Fedele

doi:10.1016/j.laa.2006.11.014

Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes

Linear Algebra and its Applications ◽

10.1016/j.laa.2006.11.014 ◽

2007 ◽

Vol 422 (2-3) ◽

pp. 553-562 ◽

Cited By ~ 1

Author(s):

Alfredo Eisinberg ◽

Giuseppe Fedele

Keyword(s):

Least Squares ◽

Explicit Solution ◽

Approximation Problem ◽

Least Squares Approximation

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The best least squares approximation problem for a 3-parametric exponential regression model

The ANZIAM Journal ◽

10.1017/s1446181100011901 ◽

2000 ◽

Vol 42 (2) ◽

pp. 254-266 ◽

Cited By ~ 7

Author(s):

D. Jukić ◽

R. Scitovski

Keyword(s):

Regression Model ◽

Least Squares ◽

Approximation Problem ◽

Existence Problem ◽

Least Squares Approximation ◽

Exponential Regression ◽

Exponential Regression Model

AbstractGiven the data (pi, ti, fi), i = 1,…,m, we consider the existence problem for the best least squares approximation of parameters for the 3-parametric exponential regression model. This problem does not always have a solution. In this paper it is shown that this problem has a solution provided that the data are strongly increasing at the ends.

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Fuzzy Least Squares Approximation Using Fuzzy Polynomial

Mathematical Problems in Engineering ◽

10.1155/2021/9979544 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Kun Liu ◽

Xiaobin Guo

Keyword(s):

Least Squares ◽

Approximation Theory ◽

Numerical Approximation ◽

Original Problem ◽

Fuzzy Numbers ◽

Approximation Problem ◽

Simple Approach ◽

Least Squares Approximation ◽

Numerical Examples ◽

Function Relation

In this paper, the fuzzy polynomial is introduced and applied to investigate the least squares approximation problem based on LR fuzzy numbers. A new and simple approach to solve the original problem is constructed by using approximate fuzzy polynomial. Two numerical examples are given to illustrate the proposed method. Since a large number of data exist as an uncertain property and need a function relation to reflect the laws between different variables, our results enrich fuzzy numerical approximation theory.

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