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 matrixx
of size n by t.- apply_t
A'*x
for a matrixx
of size n by t.- solve
A \ b
for a matrixb
of size n by t.- solve_t
A' \ b
for a matrixb
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 satisfyingnorm (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