Special section on recent progress in verified numerical computations

Abstract

Verified numerical computations play important roles for rigorously solving systems of equations arising in various scientific problems. Following the previous special section on verified numerical computations published in Vol.2 No.1 (2011), this special section is devoted to self-validating methods and computer-assisted proofs, which have attracted attention of researchers in a wide spectrum of science and engineering. The following variety of topics is presented: error-free transformation for matrix multiplication, verified solutions of linear systems, verification methods and their related topics for ordinary and partial differential equations, a topological computation approach to the interior crisis bifurcation, and verified computation for the linking number of links. The guest editors believe that this special section invites many readers to the frontier of this emerging research field. They would like to express their sincere thanks to all authors for their contributions. They also thank the reviewers and the secretaries of this special section, especially Takashi Hisakado (Kyoto University), Kenta Kobayashi (Hitotsubashi University) and Katsuhisa Ozaki (Shibaura Institute of Technology), and the editorial staff of NOLTA journal for their supports on publishing this special section.