Till Örebro universitet

We propose a two-parameter family of nonsymmetric dense n x n matrices A(alpha, beta) for which LU factorization without pivoting is numerically stable, and we show how to choose alpha and beta to achieve any value of the infinity-norm condition number. The matrix A(alpha, beta) can be formed from a simple formula in O(n(2)) flops. The matrix is suitable for use in the HPL-AI Mixed-Precision Benchmark, which requires an extreme scale test matrix (dimension n > 10(7)) that has a controlled condition number and can be safely used in LU factorization without pivoting. It is also of interest as a general-purpose test matrix.