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compute_LSQF.m
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compute_LSQF.m
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%% compute_LSQF
%
% Description:
% Function to compute the LS-QF points and weights
%
% Author: Jan Glaubitz, J. Nordström, and P.Öffner
% Date: Mar. 16, 2022
%
% INPUT:
% x_L, x_R : domain boundaries
% span : spanning set of G = (FF)'
% m : corresponding moments
% points : type of data points
%
% OUTPUT:
% x : vector of points
% w : vector of weights
function [ x, w] = compute_LSQF( x_L, x_R, span, m, points )
L = length(m); % number of basis functions (dimension of G)
N = max([floor(L/2), 2]); % dimension of F for later use 1
%% routine to determine a nonnegative LS-CF
exactness_error = 1; w_min = -1;
tol_exactness = 1e-14; % tolerance for the exactness condition
while w_min < 1e-14 || exactness_error > tol_exactness
%% data points and matrix G
x = generate_points( points, x_L, x_R, N ); % points
G = zeros(L,N);
for n=1:N
G(:,n) = span(x(n));
end
%% Compute the LS weights
w = lsqminnorm(G,m); % indirect computation using optimization tools
w_min = min(w); % their smallest value
exactness_error = norm( G*w - m )^2/L;
N = N+1; % increase the number of data points
end
end