DSP Blockset

Cholesky Inverse

Compute the inverse of a Hermitian positive definite matrix using Cholesky factorization.

Library

Math Functions / Matrices and Linear Algebra / Matrix Inverses

Description

The Cholesky Inverse block computes the inverse of the Hermitian positive definite input matrix S by performing Cholesky factorization.

L is a lower triangular square matrix with positive diagonal elements and L^* is the Hermitian (complex conjugate) transpose of L. Only the diagonal and upper triangle of the input matrix are used, and any imaginary component of the diagonal entries is disregarded. Cholesky factorization requires half the computation of Gaussian elimination (LU decomposition), and is always stable. The output is always sample-based.

The algorithm requires that the input be Hermitian positive definite. When the input is not positive definite, the block reacts with the behavior specified by the Non-positive definite input parameter. The following options are available:

• Ignore - Proceed with the computation and do not issue an alert. The output is not a valid inverse.
• Warning - Display a warning message in the MATLAB command window, and continue the simulation. The output is not a valid inverse.
• Error - Display an error dialog box and terminate the simulation.

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

References

Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

See Also

Cholesky Factorization	DSP Blockset
Cholesky Solver	DSP Blockset
LDL Inverse	DSP Blockset
LU Inverse	DSP Blockset
Pseudoinverse	DSP Blockset
inv	MATLAB

See Inverting Matrices for related information.

Cholesky Factorization

Cholesky Solver