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 ...

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 ...

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 ...

A fully derivative-free spectral residual method for solving large-scale nonlinear systems of equations is presented. It uses in a systematic way the residual vector as a search direction, a spectral ...

Simultaneous equations Simultaneous examples with no common coefficients Creating and solving simultaneous equations Simultaneous equations with linear and quadratic Solving simultaneous equations ...

Looking for the answers to ax² + bx + c = 0? A mathematician has rediscovered a technique that the ancient Babylonians used. By Kenneth Chang and Jonathan Corum The quadratic equation has frustrated ...

Look at the National 4 factorising section before continuing. When a question asks you to 'solve' a quadratic equation, this means that you are to find the roots of the quadratic. In other words, ...