Efficient Algorithms and Implementation for Error-Free Computation Using P-adic

Our research team including graduate students both in Computer Science and Mathematics has been developing P-adic Exact Scientific Computational Library (ESCL) for rational matrix operations. The effort has been focusing on converting all rational number operations to integer calculation, and fully taking the advantage of fast integer multiplication of modern computer architectures. By properly selecting prime numbers as the bases and practically choosing the length r for P-adic expansion of rational numbers, we have shown some promising results for large matrix operations, such as matrix multiplication and inverse. Dixon algorithm and his improved version, we call it Generalized Dixon (or Dixon-Krishnamurthy) algorithm, which combines Dixon algorithm with Krishnamurthy algorithm, has been developed, which can be extended to various matrix computations.