F07PJF (DSPTRI) computes the inverse of a real symmetric indefinite matrix
A, where
A has been factorized by
F07PDF (DSPTRF), using packed storage.
F07PJF (DSPTRI) is used to compute the inverse of a real symmetric indefinite matrix
A, the routine must be preceded by a call to
F07PDF (DSPTRF), which computes the Bunch–Kaufman factorization of
A, using packed storage.
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion
IMA J. Numer. Anal. 12 1–19
The computed inverse
X satisfies a bound of the form
- if UPLO='U', DUTPTXPU-I≤cnεDUTPTXPU+DD-1;
- if UPLO='L', DLTPTXPL-I≤cnεDLTPTXPL+DD-1,
cn is a modest linear function of
n, and
ε is the
machine precision.
The complex analogues of this routine are
F07PWF (ZHPTRI) for Hermitian matrices and
F07QWF (ZSPTRI) for symmetric matrices.
This example computes the inverse of the matrix
A, where
Here
A is symmetric indefinite, stored in packed form, and must first be factorized by
F07PDF (DSPTRF).