I have to calculate some Fredholm's determinant (FD) for that I found one work (arXiv:0904.1581), where the algorithm for calculating the FD was described. I was trying to repeat the following code from the mentioned work (see page 39 from arXiv:0904.1581): [w, x] = ClenshawCurtis(0, inf, m);
K1 = @(x,y) airy((x + y) / 2) / 2;
F10 = det(eye(m) - (w2' * w2) .* K1(xi, xj))
>> F10 = 0.831908066202953
and
F20 = det(eye(m) - (w2' * w2) .* KAi(x, x))
>> F20 = 0.969372828355262
The function ClenshawCurtis() has the following code:
function [w,c] = ClenshawCurtis(a, b, m)
c = cos((0 : m) * pi / m);
M = [1 : 2 : m-1]'; l = length(M); n = m - l;
v0 = [2 ./ M ./ (M-2); 1 / M(end); zeros(n, 1)];
v2 = -v0(1 : end - 1) - v0(end : -1 : 2);
g0 = -ones(m, 1); g0(1 + l) = g0(1 + l) + m; g0(1 + n) = g0(1 + n) + m;
g = g0 / (m ^ 2 + mod(m, 2));
w = ifft(v2 + g); w(m + 1) = w(1);
c = ((1 - c) / 2 * a + (1 + c) / 2 * b)';
And the expression for the @AiryKernel is given in arXiv:0904.1581 on page 2, formula (1.6). In could be defined as function fun = test(x, y)
fun = ( airy(x) .* airy(1, y) - airy(y) .* airy(1, x) ) ./ (x-y);
fun = ( airy(x) .* airy(1, y) - airy(y) .* airy(1, x) ) ./ (x - y);
When I try to run the same code, I get F10 = Nan and F20 = Nan.
What could be the problem?
