Phenomena observed in strongly correlated electron systems, such as magnetism, superconductivity in copper oxides and organic materials, metal-insulator transitions, have attracted considerable interest for their novel physical properties. Because of the complexities of problems, most are still far from theoretical understandings. The aims of our studies are, therefore, to propose new ideas for the underlying mechanisms of the phenomenon mentioned above, to predict new properties, and to find solutions for their mathematical models making full use of a large-scale computer system.