Accurate and verified numerical computation of the matrix determinant

This paper is concerned with the numerical computation of the determinant of matrices. An algorithm for rigorously enclosing the determinant of a matrix is proposed, especially for extremely ill‐conditioned cases. To achieve it, an accurate algorithm for inverse LU factorisation is used. Then accurate and verified results of the determinant can be efficiently obtained for a wide range of problems. An algorithm for computing the exact value of the determinant of an integer matrix is also proposed. Numerical results are presented showing the performance of the proposed algorithms.