Some new results regarding spikes and a heuristic for spike construction (Q1315413)

This paper discusses the problem of minimizing the number of columns with superdiagonal nonzeroes (spiked columns) in a square, nonsingular linear system of equations solved by Gaussian elimination. The author focuses on a class of min-spike heuristics in which the rows and columns of the coefficient matrix are first permuted to a block lower-triangular form. Then the number of spiked columns in each irreducible block and their heights above the diagonal are minimized heuristically.