Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

Computations that involve matrix algorithms are happening everywhere in the world at every moment in time, whether these be embedded in the training of neural networks in data science, in computer ...

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 ...

PITTSBURGH—Computer scientists at Carnegie Mellon University have devised an innovative and elegantly concise algorithm that can efficiently solve systems of linear equations that are critical to such ...

This is a preview. Log in through your library . Abstract We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is ...