The MATLAB function sprandsym generates a random symmetric matrix and will additionally make the matrix positive definite. The statement generates a sparse random symmetric positive definite matrix of...

The MATLAB function sprandsym generates a random symmetric matrix and will additionally make the matrix positive definite. The statement

generates a sparse random symmetric positive definite matrix of size
 where density is the fraction of nonzeros, and the reciprocal of rc is the exact condition number. Using spransym, generate a sparse symmetric positive definite matrix of dimension
 with
 zeros, and condition number of
 Execute
 and preconditioned
using random
 random

₀
 tol and numiter
 For preconditioned
 use incomplete Cholesky with droptol
 Compare the time required and the resulting residual.

      For the remaining problems, unless stated otherwise, use

₀
 and let
 be a random
 vector.