Zhiqiang Cai, Jan Mandel, Steve McCormick, Multigrid Methods for Nearly Singular Linear Equations and Eigenvalue Problems, SIAM Journal on Numerical Analysis, Vol. 34, No. 1 (Feb., 1997), pp. 178-200 ...

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 ...