One breakthrough came in 2010, when Dominic Berry, now at Macquarie University in Sydney, built the first algorithm for solving linear differential equations exponentially faster on quantum, rather ...

We study the compactness of a sequence of weak solutions to the (p-th power) nonlinear Klein-Gordon equation with uniform natural energy bounds. A refinement of the Rellich's Theorem of compact ...

Carpathian Journal of Mathematics, Vol. 31, No. 1 (2015), pp. 11-30 (20 pages) We use the method of recurrent functions to provide a new semilocal convergence analysis for secant-like methods in order ...

Parameter embedding methods, also known as continuation methods, are robust and accurate numerical techniques employed to solve non-linear algebraic equations. They are used to solve equations that ...

A system of nonlinear equations is harder to solve than you think—and more of a puzzle than a math problem. Puzzles like this require you to look and find the one loose end you can pull to ...

Mathematicians have devised a new way to solve higher-order polynomial equations, ushering in a 'dramatic revision of a basic chapter in algebra'.