LDL Factorization (DSP Blockset)

DSP Blockset

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LDL Factorization

See Also

Factor a Hermitian positive definite matrix into lower, upper, and diagonal components.

Library

Linear Algebra, in Math Functions

Description

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

where L is a lower triangular square matrix with unity diagonal elements, D is a diagonal matrix, and L^H denotes the Hermitian transpose of L. The block's output is a composite matrix with lower triangle L, diagonal D and upper triangle L^H. The format is shown below for a 5-by-5 matrix.

Example:

LDL factorization requires half the computation of Gaussian elimination (LU decomposition), and is always stable. It is more efficient that Cholesky factorization because it avoids computing the square roots of the diagonal elements.

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References

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