Breakthrough in numerical analysis and numerical computation related with infinitely-precision arithmetic

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We have shown some new results aimed to accurate scientific computationsbased on effective use of infinitely-precision arithmetic. The project study has been carried out both by theoretical approaches and computationalones. In the theory of numerical analysis, convergence of an abstract difference scheme is proved with a technique of the Banach scale, and numerical instability of difference schema are discussed from a viewpoint of proper meaning of the CFL condition. In computation, we have obtained accurate numerical results for the problems appeared in the particle physics and the eigen-value problems. The GPGPU programmingsare also discussed in order to realize fast computational environment.