Function Reference
— Function File: [est, v] = condest (a, t)
— Function File: [est, v] = condest (a, solve, solve_t, t)
— Function File: [est, v] = condest (apply, apply_t, solve, solve_t, n, t)

Estimate the 1-norm condition number of a matrix matrix A using t test vectors using a randomized 1-norm estimator. If t exceeds 5, then only 5 test vectors are used.

If the matrix is not explicit, e.g. when estimating the condition number of a given an LU factorization, condest uses the following functions:

apply
A*x for a matrix x of size n by t.
apply_t
A'*x for a matrix x of size n by t.
solve
A \ b for a matrix b of size n by t.
solve_t
A' \ b for a matrix b of size n by t.

The implicit version requires an explicit dimension n.

condest uses a randomized algorithm to approximate the 1-norms.

condest returns the 1-norm condition estimate est and a vector v satisfying norm (A*v, 1) == norm (A, 1) * norm (v, 1) / est. When est is large, v is an approximate null vector.

References:

  • Nicholas J. Higham and Fran