How can I perform the modified Cholesky factorization in MATLAB?

I would like to perform a modified Cholesky factorization for matrices that are not necessarily positive definite in MATLAB.

Answer 1

[MathWorks Support Team]

The ability to perform the modified Cholesky factorization is not available in MATLAB.

However, a third-party MATLAB file is available on the MATLAB Central File Exchange:

https://www.mathworks.com/matlabcentral/fileexchange/47-ldlt

Please note that any questions relating to files downloaded from MATLAB Central should be directed to the author(s) of those files.

Starting with MATLAB R2006b, the LDL function is available which can achieve Cholesky decomposition without taking the square root.

However the assumption that the input matrix is square, symmetric, positive definite still holds.

https://www.mathworks.com/help/matlab/ref/ldl.html

Documentation for the ICHOL function which performs incomplete Cholesky factorization is available at the following link:

https://www.mathworks.com/help/matlab/ref/ichol.html