As the drop tolerance decreases when using Cholesky preconditioning, the matrix becomes more dense. Using spy, graph the complete Cholesky factor for the matrix in the software distribution. ...

As the drop tolerance decreases when using Cholesky preconditioning, the matrix

becomes more dense.

Using spy, graph the complete Cholesky factor for the matrix

in the software distribution.

Computing an incomplete Cholesky factorization of ROOF is particularly difficult. Try icholesky and then ichol with no drop tolerance.

Using a drop tolerance will make ichol successful. Using spy, demonstrate the increase in density using the MATLAB function ichol with drop tolerances of

⁻⁴
and

⁻⁵

What happens when you try drop tolerances of

⁻²
and

⁻³