F07WJF (DPFTRI) computes the inverse of a real symmetric positive definite matrix using the Cholesky factorization computed by
F07WDF (DPFTRF) stored in Rectangular Full Packed (RFP) format.
The RFP storage format is described in
Section 3.3.3 in the F07 Chapter Introduction.
F07WJF (DPFTRI) is used to compute the inverse of a real symmetric positive definite matrix
A, the routine must be preceded by a call to
F07WDF (DPFTRF), which computes the Cholesky factorization of
A.
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion
IMA J. Numer. Anal. 12 1–19
Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion
ACM Trans. Math. Software 37, 2 The computed inverse
X satisfies
where
cn is a modest function of
n,
ε is the
machine precision and
κ2A is the condition number of
A defined by
The complex analogue of this routine is
F07WWF (ZPFTRI).
This example computes the inverse of the matrix
A, where
Here
A is symmetric positive definite, stored in RFP format, and must first be factorized by
F07WDF (DPFTRF).