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 ...

Eigenvalue problems are a cornerstone of modern applied mathematics, arising in diverse fields from quantum mechanics to structural engineering. At their heart, these problems seek scalar values and ...

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 ...