Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

Some algorithms based upon a projection process onto the Krylov subspace $K_m = \operatorname{Span}(r_0, Ar_0, \ldots, A^{m - 1}r_0)$ are developed, generalizing the ...

Let Q be an n x n symmetric matrix with integral entries and with det Q ≠ O, but not necesarily positive definite. We describe a generalized LLL algorithm to reduce this quadratic form. This algorithm ...