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C++ API

: cest = condest (A)

: cest = condest (A, t)

: cest = condest (A, solvefun, t, p1, p2, …)

: cest = condest (Afcn, solvefun, t, p1, p2, …)

: [cest, v] = condest (…)

Estimate the 1-norm condition number of a square matrix A using t test vectors and a randomized 1-norm estimator.

The optional input t specifies the number of test vectors (default 5).

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

• - Afcn which must return
  • the dimension n of a, if flag is "dim"
  • true if a is a real operator, if flag is "real"
  • the result a * x, if flag is "notransp"
  • the result a' * x, if flag is "transp"
• - solvefun which must return
  • the dimension n of a, if flag is "dim"
  • true if a is a real operator, if flag is "real"
  • the result a \ x, if flag is "notransp"
  • the result a' \ x, if flag is "transp"

The parameters p1, p2, … are arguments of Afcn (flag, x, p1, p2, …) and solvefcn (flag, x, p1, p2, …).

The principal output is the 1-norm condition number estimate cest.

The optional second output is an approximate null vector when cest is large; it satisfies the equation norm (A*v, 1) == norm (A, 1) * norm (v, 1) / est.

Algorithm Note: condest uses a randomized algorithm to approximate the 1-norms. Therefore, if consistent results are required, the "state" of the random generator should be fixed before invoking condest.

References:

• N.J. Higham and F. Tisseur, A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra. SIMAX vol 21, no 4, pp 1185-1201. http://dx.doi.org/10.1137/S0895479899356080
• N.J. Higham and F. Tisseur, A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra. http://citeseer.ist.psu.edu/223007.html

See also: cond, norm, normest1, normest.

Package: octave