Synthetical development of fast numerical methods for solving large-scale linear systems which arise g from the field of computational science and engineerin

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The target of this project is synthetically to develop fast numerical methods for solving large-scale linear systems which arise from the field of computational science and engineering. Throughout the whole of this project, we completed almost the target.The research results of this project are concluded as follows.1. The circumstance of applications which lead large linear systems was investigated by all of numbers.2. The coefficient matrix of linear systems was classified from size, structure and algebra.3. The convergent property of new methods GPBi-CG(ω) and GPBi-CG was evaluated through many test problems.4. The convergence theory for singular linear systems was studied.5. Several kinds of preconditioning technique was studied.6. A new fast and basic method, so-called Bi-CR, was proposed.7. A new systems of parallel computer was built for this project.8. A new web server system for large linear system was built almost.