This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Large-Scale Scientific Computations, LSSC 2003, held in Sozopol, Bulgaria in June 2003. The 50 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on preconditioning techniques, Monte Carlo methods and quasi-Monte-Carlo methods, set-value of numerics and reliable computing, environmental modeling, and large-scale computations for engineering problems.