FLINT3.7.0-dev
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_arb_mat_ldl_inplace, _arb_mat_ldl_golub_and_van_loan, arb_mat_ldl

Synopsis#include <flint/arb_mat.h>
int _arb_mat_ldl_inplace(arb_mat_t A, slong prec)source
int _arb_mat_ldl_golub_and_van_loan(arb_mat_t A, slong prec)source
int arb_mat_ldl(arb_mat_t res, const arb_mat_t A, slong prec)source

Compute the decomposition A=LDLTA = LDL^T with LL unit lower triangular and DD diagonal, stored in res: the strict lower triangle holds LL and the diagonal holds DD. Return nonzero if all entries of DD are certainly positive, which proves that AA is positive definite, and zero otherwise. The underscore versions work in place and leave the strict upper triangle undefined; the default uses Algorithm 4.1.2 of [GVL1996] (_arb_mat_ldl_golub_and_van_loan).

Guides#

References#

  • [GVL1996] G. H. Golub and C. F. Van Loan, Matrix Computations, third edition, Johns Hopkins University Press (1996).
Cite this page

The FLINT team, “_arb_mat_ldl_inplace, _arb_mat_ldl_golub_and_van_loan, arb_mat_ldl (arb_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_mat/_arb_mat_ldl_inplace.html (generated 2026-11-02).