Abstract. The DE transformation used in the DE quadrature formulas is applied to various numerical computations other than numerical integration using the Sinc approximation. On the other hand, the IMT-type transformations are also used in numerical integration, which are expected to be applied to various numerical using the Sinc approximation for periodic functions. In this paper, the author propose a numerical method of indefinite integration based on the above idea.

Abstract. In the case of discrete data, we propose a novel method for both model selection and parameter estimation by detecting independence copulas from a model whose dependence structure is constructed by a Dvine t copula using the Reversible Jump Markov Chain Monte Carlo together with the Data Augmentation. It was shown that the proposed method has sufficient parameter estimation accuracy.

Abstract. For solving nonlinear scalar equations, multipoint iterative methods without memory are the most commonly used algorithms. For these methods, there exists a well-known conjecture (Kung-Traub's conjecture): the methods requiring m+1 (m ≥ 1) function evaluations per iteration have order of convergence at most 2^m. This paper shows that among the maximum order methods those of m=1 are being most effective, if the methods are executed by variable multiple precision arithmetic. As a result, the methods of 2nd order, including Newton's method, are fastest. On the contrary, the methods of larger m are shown to be faster when the precision is fixed.