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 ...

SIAM Journal on Numerical Analysis, Vol. 7, No. 1 (Mar., 1970), pp. 47-66 (20 pages) Linear one step methods of a novel design are given for the numerical solution of stiff systems of ordinary ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Solving an equation means finding the value or values for which the two expressions on each side of the equals sign are equal. One of the most common methods used to solve equations is the balance ...

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 ...

An equation is a statement with an equals sign, stating that two expressions are equal in value, for example: \(3x + 5 = 11\). Solving an equation means finding the value or values for which the two ...

A mathematician at Carnegie Mellon University has developed an easier way to solve quadratic equations. The mathematician hopes this method will help students avoid memorizing obtuse formulas. His ...