How LU decomposition works part2(Machine Learning)

1. A matrix with sums of Catalan numbers — LU-decomposition and determinant(arXiv)

Author : Helmut Prodinger

Abstract : Following Benjamin et al., a matrix with entries being sums of two neighbouring Catalan numbers is considered. Its LU-decomposition is given, by guessing the results and later prove it by computer algebra, with lots of human help. Specializing a parameter, the determinant turns out to be a Fibonacci number with odd index, confirming earlier results, obtained back then by combinatorial methods.

2.Some combinatorial matrices and their LU-decomposition (arXiv)

Author : Helmut Prodinger

Abstract : Three combinatorial matrices are considered and their LU-decompositions were found. This is typically done by (creative) guessing, and necessary proofs are more or less routine calculations.