Improvement of selection formulas of mesh size and truncation numbers for the double-exponential formula

抄録

The double-exponential formula is known as a very efficient quadrature formula. An important point in eliciting its high performance is properly selecting mesh size and truncation numbers depending on a given positive integer. However, the standard selection formulas are not optimal, and there is room for improvement. In this paper, we propose improved selection formulas that reduce the error of the double-exponential formula. We also present a computable error bound of the modified double-exponential formula.