We analyze necessary and sufficient conditions on a nonsingular matrix A such that, for any initial vector r₀, an orthogonal basis of the Krylov subspaces ${\cal K}_{n}(A,r_{0})$ is generated by a ...

SIAM Journal on Numerical Analysis, Vol. 43, No. 3 (2006), pp. 1321-1347 (27 pages) This paper develops and investigates iterative tensor methods for solving large-scale systems of nonlinear equations ...

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 ...

The Nature Index 2024 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...