ALGORITMY (Algorithms) represents the oldest Central-European series of international high level scientific meetings devoted to applied mathematics and numerical methods in computational sciences and engineering. It has been traditionally organized in the High Tatra Mountains, Slovakia (see ALGORITMY 2009, ALGORITMY 2005, ALGORITMY 2002) by the Slovak University of Technology in Bratislava in cooperation with Comenius University in Bratislava and Slovak and Czech Academy of Sciences. Following this old tradition, the 19th ALGORITMY conference will be devoted to computational methods, their analysis, algorithmic realization and application to real-world problems arising from, but not restricted to, natural sciences, engineering, technology, medicine and finance. The main topics of the ALGORITMY 2012 conference are: * computational fluid dynamics, nonlinear conservations laws, heat transfer and porous media flow * free boundary problems * image processing and computer vision * computer graphics and computational geometry * computational finance * computational biology and medicine * computational geosciences * optimal control and inverse problems * direct and iterative methods for large linear algebraic systems * high-scale and parallel computing * scientific visualization * software for scientific computations. In solving the above mentioned real-world problems, the main attention is given to a new development and advanced applications of modern numerical methods as finite element, finite volume and finite difference schemes, preconditioning techniques and Lagrangean and Eulerian level-set methods, applied on structured and unstructured adaptive grids.