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When floating point arithmetic is used in numerical computation, cancellation of significant digits, round-off errors and information loss cannot be avoided. In some cases it becomes necessary to use multiple precision arithmetic; however some operations of this arithmetic are difficult to implement within conventional computing environments. In this paper(More)
To verify computation results of double precision arithmetic, a high precision arithmetic environment is needed. However, it is difficult to use high precision arithmetic in ordinary computing environments without any special hardware or libraries. Hence, we designed the quadruple precision arithmetic environment QuPAT on Scilab to satisfy the following(More)
Double-double and quad-double arithmetics are effective tools to reduce the round-off errors in floating-point arithmetic. However, the dense data structure for high-precision numbers in MuPAT/Scilab requires large amounts of memory and a great deal of the computation time. We implemented sparse data types ddsp and qdsp for double-double and quad-double(More)
Based on the integrable discrete hungry Toda (dhToda) equation, the authors designed an algorithm for computing eigenvalues of a class of totally nonnegative matrices (Ann Mat Pura Appl, doi: 10.1007/s10231-011-0231-0 ). This is named the dhToda algorithm, and can be regarded as an extension of the well-known qd algorithm. The shifted dhToda algorithm has(More)