Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization

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