FLINT3.7.0-dev
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acb_mat_solve, acb_mat_solve_lu, acb_mat_solve_precond

Synopsis#include <flint/acb_mat.h>
int acb_mat_solve(acb_mat_t X, const acb_mat_t A, const acb_mat_t B, slong prec)source
int acb_mat_solve_lu(acb_mat_t X, const acb_mat_t A, const acb_mat_t B, slong prec)source
int acb_mat_solve_precond(acb_mat_t X, const acb_mat_t A, const acb_mat_t B, slong prec)source

Solve AX=BAX = B for a square matrix AA and XX, BB with mm columns. Return nonzero if AA is proved invertible, in which case X contains the exact solution for every pair of matrices in the balls AA and BB; return zero (with X undefined) if m>0m > 0 and this could not be proved. The lu version uses Gaussian elimination in ball arithmetic, the precond version preconditions with an approximate inverse [HS1967], and the default uses the lu version if n≤4n \le 4 or prec>10n\mathit{prec} > 10n and the precond version otherwise. See Solving linear systems with ball matrices.

References#

  • [HS1967] E. Hansen and R. Smith, "Interval Arithmetic in Matrix Computations, Part II", SIAM Journal of Numerical Analysis, 4(1):1-9 (1967). https://doi.org/10.1137/0704001
Cite this page

The FLINT team, “acb_mat_solve, acb_mat_solve_lu, acb_mat_solve_precond (acb_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_mat/acb_mat_solve.html (generated 2026-11-02).