Chebyshev polynomials and best approximation of some classes of functions

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Mohammad R. Eslahchi ◽  
Mehdi Dehghan ◽  
Sanaz Amani
Keyword(s):  
Polynomial Approximation ◽  
Chebyshev Polynomials ◽  
Best Approximation ◽  
The Best Approximation ◽  
Uniform Polynomial Approximation

AbstractIn this research using properties of Chebyshev polynomialswe explicitly determine the best uniform polynomial approximation of some classes of functions. In this way we present some new theorems about the best approximation of these classes.

scholarly journals On the fast approximation of point clouds using Chebyshev polynomials

2021 ◽  
Vol 15 (4) ◽  
pp. 305-317
Author(s):  
Sven Weisbrich ◽  
Georgios Malissiovas ◽  
Frank Neitzel
Keyword(s):  
Chebyshev Polynomials ◽  
Best Approximation ◽  
Point Cloud ◽  
Complex Geometry ◽  
Point Clouds ◽  
Method Of Least Squares ◽  
The Best Approximation ◽  
Chebyshev Points ◽  
Dense Point ◽  
Univariate Function

Abstract Suppose a large and dense point cloud of an object with complex geometry is available that can be approximated by a smooth univariate function. In general, for such point clouds the “best” approximation using the method of least squares is usually hard or sometimes even impossible to compute. In most cases, however, a “near-best” approximation is just as good as the “best”, but usually much easier and faster to calculate. Therefore, a fast approach for the approximation of point clouds using Chebyshev polynomials is described, which is based on an interpolation in the Chebyshev points of the second kind. This allows to calculate the unknown coefficients of the polynomial by means of the Fast Fourier transform (FFT), which can be extremely efficient, especially for high-order polynomials. Thus, the focus of the presented approach is not on sparse point clouds or point clouds which can be approximated by functions with few parameters, but rather on large dense point clouds for whose approximation perhaps even millions of unknown coefficients have to be determined.

Intracranial volume-pressure relationship in man

1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet
Keyword(s):  
Best Approximation ◽  
Continuous Monitoring ◽  
Fluid Pressure ◽  
Constant Term ◽  
Volume Index ◽  
Intracranial Volume ◽  
Content Type ◽  
The Best Approximation ◽  
Ventricular Fluid Pressure ◽  
Fine Print

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.

scholarly journals The best approximation and composition with inner functions.

1995 ◽  
Vol 42 (2) ◽  
pp. 367-378 ◽  
Author(s):  
M. Mateljević ◽  
M. Pavlović
Keyword(s):  
Best Approximation ◽  
Inner Functions ◽  
The Best Approximation

scholarly journals On one approximation of flat curves by broken lines

2021 ◽  
Vol 15 ◽  
pp. 31
Author(s):  
S.V. Babenko ◽  
V.I. Ruban
Keyword(s):  
Best Approximation ◽  
The Best Approximation ◽  
Curve Approximation

We investigate the interrelations between the error of one method of curve approximation and the error of the best approximation.

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