Abstract. For two values a and b and their approximation and , if the approximations and are inaccurate, then the sign of - can be different from that of a−b. We propose a floating-point filter for this problem. This gives a sufficient condition for the correctness of the sign using only numerical computations.

Abstract. Conjugate gradient squared (CGS)-type methods for solving nonsymmetric linear systems often have large oscillations in the residual norms, and they are known to affect the maximum attainable accuracy of approximate solutions. The oscillations may be reduced by using a residual smoothing technique. However, when using the existing implementations, the attainable accuracy of the smoothed sequences is not higher than that of the primary ones. In this paper, we propose an alternative implementation of the smoothing technique to avoid severe propagation of rounding errors, which towards to improve the attainable accuracy. Numerical experiments show the effectiveness of our proposed method.

Abstract. An untwisted loop strip is folded to make a regular tetrahedron. The folding pattern is indexed by an irreducible rational number p/q. This also simplifies the description of the family of unfoldings of the regular tetrahedron to convex polygons.

Abstract. This paper shows a formulation of a deformable condition in the singular flat state of a rigid origami model by taking account of the second-order term. The derivation is shown as corresponding to a linkage problem. Finally, the proposed two methods are shown to be applicable for extracting a valid foldable mode with using some examples of crease-pattern on a plane surface.