Cholesky Factorization (DSP Blockset)

DSP Blockset

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Cholesky Factorization

See Also

Factor a Hermitian positive definite matrix into triangular components.

Library

Linear Algebra, in Math Functions

Description

The Cholesky Factorization block uniquely factors the Hermitian positive definite input matrix S as

where L is a lower triangular square matrix with positive diagonal elements and L^H denotes the Hermitian transpose of L. The block's output is a matrix whose lower triangle is L and whose upper triangle is L^H.

Note that L and L^H share the same diagonal in the output matrix. Cholesky factorization requires half the computation of Gaussian elimination (LU decomposition), and is always stable.

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

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

Dialog Box

Invalid input matrix: Response to non-positive definite matrix inputs.

References

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