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].

`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.

 condeig coneplot