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),'--'); …
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.
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.
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
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.
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
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 ...
The method is Chebyshev interpolation. ... X abscissas for interpolation nodes % Y ordinates for interpolation nodes % % NUMERICAL METHODS: MATLAB Programs, ...
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],
% 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 …
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.