In this paper, we show an application of hyperfunction theory to numerical integration. It is based on the remark that, in hyperfunction theory, functions with singularities such as poles, discontinuities and delta impulses are expressed in terms of complex holomorphic functions. In our method, we approximate a desired integral by approximating the complex integral which defines the desired integral as an hyperfunction integral by the trapezoidal rule. Theoretical error analysis shows that the approximation by our method converges geometrically, which is due to the fact that the approximation by the trapezoidal rule of the integral of a periodic analytic function over one period interval or the integral of an analytic function over the whole infinite interval converges geometrically. Numerical examples show that our method is efficient especially for integrals with strong end-point singularities.

An evaluation structure is a hierarchical structure of human cognition extracted from interviews based on the evaluation grid method. An evaluation structure can be defined as a directed acyclic graph (DAG) and be visualized by the Sugiyama framework that is a popular graph drawing method. In this paper, we discuss a layer assignment method that is a part of Sugiyama framework for interactive visualization of evaluation structures. We propose a novel heuristic method to approximately solve the layer assignment problem in polynomial time. We compare the performance of the proposed method with an exact method and an existing approximate solution method. It is demonstrated that the proposed method produces readable layout in a short time.