Rump, Siegfried M.Siegfried M.Rump2021-02-222021-02-222006-05-03BIT Numerical Mathematics 46 (2): 433-452 (2006)http://hdl.handle.net/11420/8891We present a computational, simple and fast sufficient criterion to verify positive definiteness of a symmetric or Hermitian matrix. The criterion uses only standard floating-point operations in rounding to nearest, it is rigorous, it takes into account all possible computational and rounding errors, and is also valid in the presence of underflow. It is based on a floating-point Cholesky decomposition and improves a known result. Using the criterion an efficient algorithm to compute rigorous error bounds for the solution of linear systems with symmetric positive definite matrix follows. A computational criterion to verify that a given symmetric or Hermitian matrix is not positive definite is given as well. Computational examples demonstrate the effectiveness of our criteria.en1572-912520062433452Springer Science + Business Media B.V.Cholesky decompositionINTLABPositive definiteRigorous error boundsSelf-validating methodsSemidefinite programmingVerificationMathematikJournal Article10.1007/s10543-006-0056-1Other