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Some of the authors design an algorithm, named the dhLV algorithm, for computing complex eigenvalues of a certain band matrix. The recursion formula of the dhLV algorithm is derived from the discrete hungry Lotka-Volterra system which is an integrable system. One of the authors proposes an algorithm, named the multiple dqd algorithm, for eigenvalues of… (More)

- Emiko Ishiwata
- 2004

In this paper, we consider the following logistic equation with piecewise constant arguments: dN (t) dt = rN (t){1 − m j=0 a j N ([t − j])}, t ≥ 0, m ≥ 1, m j=0 a j > 0, and [t] means the maximal integer not greater than t. The sequence {N n } ∞ n=0 , where N n+1 = N n exp{r(1 − m j=0 a j N n−j)}, n = 0, 1, 2, · · ·. Under the condition that the first term… (More)

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)

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)