Recent content by robertsj

This is a slightly old post, but I'll comment anyway. As for automated optimization methods, there is a plethora of recent work on all sorts of bizarre methods (ant colony, swarm, etc.). The most important methods in practice have been simulated annealing, and, to a lesser extent, genetic...

Just to clarify, backsubstitution costs n^2 flops. Full elimination costs O(n^3), but the underlying library should recognize the triangular system.

Jes1x1: I'll repeat what I noted above. Even though you could write down the exact solution by manually doing back substitution, my guess is that it would not be faster due to overhead. From what I see of your matrix, it doesn't look like you can make any significant decrease in floating point...

chiro: you're absolutely right if A were to be invertible, but that would be an unspecified constraint on A. As for assuming a nonsingular matrix, I work all the time with a method dealing with singular operators.

Under the hood, Mathematica probably already knows the matrix is lower diagonal and uses some specialized routine to perform the operation. My guess is it uses something like a highly tuned BLAS/LAPACK implementation. As for implementing your own solver, in almost all cases, it will be...

Are you sure it's true? The matrix A = \left [\begin{array}{ccc} 0 & 1 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ \end{array} \right ] has \lambda = 0 with multiplicity 3. Multiplying A by the ones vector does not, however, yield the zero vector. Perhaps you left out...

Hi all, I have a physically-motivated algorithm for which I'm trying to flesh out some basic properties analytically. In one case, I end up with a matrix of the following form: \left [\begin{array}{ccccccccc} 0 & & & & & & & & \\...