Array Valued Integral Problem - Tikhonov Regularization
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I am working on a script to perform Tikhonov Regularization on experimental data. I need to first set up an operator matrix K (this is the problem) that transforms the desired solution f (a vector) into the experimental data b (also a vector), ie, Kf=b. In other words, I aim to solve a Fredholm Integral equation of the first kind using the Tikhonov method.
K depends on two parameters, r (distance) and t (time). At each r and t, the integral along z should return a scalar to populate that element in the array.
I am encountering this error message: Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.5e-01. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
The relevant code:
b_magn = 9.27400968E-24; %bohr magneton (J/T)
gamma_e = 1.760859708E11; %gyromagnetic ratio of electron (rad/(s*T))
planck = 6.62606957E-34; %planck's constant (J*s)
hbar = planck/(2*pi); %planck's reduced constant
r = [1 : .01 : 11]; %nm
t = [0 : .01 : 10]; %us
omega_d = gamma_e^2*hbar./(r*1e-9).^3;
for it = 1:numel(t);
for ir = 1:numel(r);
y = @(z) cos((1-3.*z.^2)*(t(it)*1e-6).*omega_d(ir));
K = integral(y,0,1,'Arrayvalued',true); %operator matrix
end
end
[U,S,V] = svd(K);
The function y and the bounds of integration seem innocuous enough. I do not know where I am running into issue.
Thanks!
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