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# condestsp

estimate the condition number of a sparse matrix

### Syntax

[K1] = condestsp(A, LUp, t) [K1] = condestsp(A, LUp) [K1] = condestsp(A, t) [K1] = condestsp(A)

### Arguments

- A
a real or complex square sparse matrix

- LUp
(optional) a pointer to (umf) LU factors of A obtained by a call to umf_lufact ; if you have already computed the LU (= PAQ) factors it is recommended to give this optional parameter (as the factorization may be time consuming)

- t
(optional) a positive integer (default value 2) by increasing this one you may hope to get a better (even exact) estimate

- K1
estimated 1-norm condition number of A

### Description

Give an estimate of the 1-norm condition number of the sparse matrix A by Algorithm 2.4 appearing in :

"A block algorithm for matrix 1-norm estimation with an application to 1-norm pseudospectra" Nicholas J. Higham and Francoise Tisseur Siam J. Matrix Anal. Appl., vol 21, No 4, pp 1185-1201

Noting the exact condition number `K1e = ||A||_1 ||A^(-1)||_1`

,
we have always `K1 <= K1e`

and this estimate gives in most case
something superior to `1/2 K1e`

### Examples

A = sparse( [ 2 3 0 0 0; 3 0 4 0 6; 0 -1 -3 2 0; 0 0 1 0 0; 0 4 2 0 1] ); K1 = condestsp(A) // verif by direct computation K1e = norm(A,1)*norm(inv(full(A)),1) // another example [A] = ReadHBSparse(SCI+"/modules/umfpack/demos/arc130.rua"); K1 = condestsp(A) // this example is not so big so that we can do the verif K1e = norm(A,1)*norm(inv(full(A)),1) // if you have already the lu factors condestsp(A,Lup) is faster // because lu factors are then not computed inside condestsp Lup = umf_lufact(A); K1 = condestsp(A,Lup) umf_ludel(Lup) // clear memory

### See also

- umf_lufact — lu factorization of a sparse matrix
- rcond — inverse condition number

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