Hi Shahin,
To use the regularization tools in MATLAB, follow these steps:
1. Download the "Regularization Tools" package from the following MATLAB File Exchange link: https://mathworks.com/matlabcentral/fileexchange/52-regtools
2. Use functions like "tikhonov", "lsqr", or "cgls" to solve regularization problems. For example:
[x, rho, eta] = tikhonov(A, b, alpha);
Addressing your second query, the "phillips" and "foxgood" functions create synthetic test problems that simulate ill-posed conditions, allowing for the evaluation of various regularization methods.
Phillips Function: Generates the "Phillips test problem," a benchmark for assessing regularization techniques. Use:
[A, b, x_true] = phillips(n);
Here, A is the coefficient matrix, "b" is the right-hand side vector, and "x_true" is the true solution vector, with "n" specifying the problem size.
Foxgood Function: Creates the "Foxgood test problem," offering a different structure and challenge compared to the Phillips problem. Use:
[A, b, x_true] = foxgood(n);
Like the "phillips" function, "A" is the coefficient matrix, "b" is the right-hand side vector, and "x_true" is the true solution vector, with "n" indicating the size of the problem. This function provides an alternative benchmark for comparing regularization methods.
For further reading and examples, refer to the following MathWorks File Exchange link:
Hope this helps.
