sin(x) power series

sin_fit.m

% Compute the power series of sin(x) using
% linear least-squares.

samples = 1000000;
degree = 10;
noise = 0.1;

xs = stdnormal_rnd(samples, 1);
xPowers = zeros(samples, degree);
for d = 1:degree
  xPowers(:,d) = xs.^d;
end

target = sin(xs) + noise*stdnormal_rnd(samples, 1);

% Least squares regression.
actual = xPowers \ target

% Verify using the actual power series.
expected = zeros(degree, 1);
for i = 1:degree
  if mod(i,2) == 1
    expected(i) = 1/factorial(i);
    if mod(i,4) != 1
      expected(i) *= -1;
    end
  end
end
mse = mean((actual-expected).^2)