Dec 09, 2018 · Interpolation Using Chebyshev Polynomials CHEBYSHEVis a MATLAB library which constructs the Chebyshev interpolant to a function. Note that the user is not free to choose the interpolation points. algorithm. In the standard case, in which the interpolation interval is [-1,+1],
09.12.2018 · chebyshev, a MATLAB code which constructs the Chebyshev interpolant to a function.. Note that the user is not free to choose the interpolation points. Instead, the function f(x) will be evaluated at points chosen by the algorithm.
% Sample calls % [C] = cheby('f',n) % [C,X,Y] = cheby('f',n) % [C,X,Y] = cheby('f',n,a,b) % Inputs % f name of the function % n degree of the Chebyshev interpolation polynomial % a left endpoint of the interval % b right endpoint of the interval % Return % C coefficient list for the Chebyshev interpolation polynomial % X abscissas for interpolation nodes % Y ordinates for interpolation …
Also, Chebyshev approximation and its relation to polynomial interpolation at equidistant nodes have been discussed on the example which is very similar with Runge’s function. Key words: interpolation, Lagrangian polynomial, MATLAB, Equidistant network, Chebyshev polynomials
09.12.2018 · CHEBYSHEV is a MATLAB library which constructs the Chebyshev interpolant to a function.. Note that the user is not free to choose the interpolation points. Instead, the function f(x) will be evaluated at points chosen by the algorithm.
Evaluate Chebyshev Polynomials with Floating-Point Numbers. Floating-point evaluation of Chebyshev polynomials by direct calls of chebyshevT is numerically stable. However, first computing the polynomial using a symbolic variable, and then substituting variable-precision values into this expression can be numerically unstable.
Dec 09, 2018 · chebyshev , a MATLAB code which constructs the Chebyshev interpolant to a function. Note that the user is not free to choose the interpolation points. Instead, the function f (x) will be evaluated at points chosen by the algorithm.
The method is Chebyshev interpolation. ... X abscissas for interpolation nodes % Y ordinates for interpolation nodes % % NUMERICAL METHODS: MATLAB Programs, ...
Chebyshev polynomials of the first kind are defined as Tn(x) = cos (n*arccos (x)). These polynomials satisfy the recursion formula Chebyshev polynomials of the first kind are orthogonal on the interval -1 ≤ x ≤ 1 with respect to the weight function . Chebyshev polynomials of the first kind are special cases of the Jacobi polynomials
10.09.2019 · % find 10 Chebyshev nodes and mark them on the plot n = 10; k = 1:10; % iterator xc = cos((2*k-1)/2/n*pi); % Chebyshev nodes yc = f(xc); % function evaluated at Chebyshev nodes hold on; plot(xc,yc,'o') % find polynomial to interpolate data using the Chebyshev nodes p = polyfit(xc,yc,n-1); % gives the coefficients of the polynomial of degree 10 plot(x,polyval(p,x),'--'); …
Dec 08, 2014 · Interpolation Matlab code for Chebyshev interpolation, including Smolyak algorithm This repository includes Matlab code that I have written for multidimensional function interpolation with Chebyshev polynomials. It includes a implementation of the isotropic and the anisotropic Smolyak algorithms, as described by Judd et al. 2014.
Sep 11, 2019 · Interpolate the Runge function of Example 10.6 at Chebyshev points for n from 10 to 170 in increments of 10. Calculate the maximum interpolation error on the uniform ...