condest (MATLAB Functions)

MATLAB Function Reference

condest

1-norm condition number estimate

Syntax

```
c = condest(A)
[c,v] = condest(A)
```

Description

c = condest(A) computes a lower bound C for the 1-norm condition number of a square matrix A.

c = condest(A,t) changes t, a positive integer parameter equal to the number of columns in an underlying iteration matrix. Increasing the number of columns usually gives a better condition estimate but increases the cost. The default is t = 2, which almost always gives an estimate correct to within a factor 2.

[c,v] = condest(A) also computes a vector v which is an approximate null vector if c is large. v satisfies norm(A*v,1) = norm(A,1)*norm(v,1)/c.

Note condest invokes rand. If repeatable results are required then invoke rand('state',j), for some j, before calling this function.

This function is particularly useful for sparse matrices.

condest uses block 1-norm power method of Higham and Tisseur [1].

See Also

cond, norm, normest

Reference

[1] Higham, N. J. and F. Tisseur, "A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra," SIAM Journal Matrix Anal. Appl., Vol. 21, No. 4, 2000, pp.1185-1201.

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