We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first finds a short vector ...

Santosh Vempala, along with Richard Peng, came up with a new, faster way of solving certain linear equations, “the workhorse of modern computation” according to Vempala.

This new equation is split into a principal part, which is explicitly invertible, and a compact perturbation. Then a discrete Galerkin method that takes special advantage of the splitting of the ...