What is the computational complexity of solving a system of equations using A\b?

When dividing matrices, what is the order of the number of operations (big O notation)? Is this generally dependent on the dimensions of the matrcies or something else?

Answer 1

[Walter Roberson]

See https://www.mathworks.com/help/matlab/ref/mldivide.html#bt4jslc-6 which has a flow chart of which solver will get chosen in which situation.

After that you would look up the complexity of each solver of interest to you. For example https://stackoverflow.com/questions/23112943/time-complexity-of-cholesky-decomposition-for-the-ldl-form