This paper introduces fundamental concepts of computer arithmetic and high-accurate numerical computations. In paricular the effective use of multiple-precision arithmetic is proposed with high-accurate stabilization and high-order discretization. Rounding error, which prevents high-accurate numerical computation, is also discussed with examples.

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This paper presents an optimal control method which is based on a newly established framework of control problem and its application for steer-by-wire system. This framework is composed of obtaining the ideal characteristics of the system for a given criteria function and solving the equations of motion by using the inverse of ideal characteristics function as an optimal control law. The criteria function is defined as the combination of energy flow equation and performance measures. Minimization of the criteria function yields the ideal characteristics. In this paper, the necessary condition for optimality is given and the optimality is proven. Steer-by-wire system has the range of the front steer angle about ±30 deg. It is not easy to find the technique theoretically for controlling the control variable region in such a large steering angle. This control theory is applied to steer-by-wire and it is clarified that an emergence pattern was generated in the wave form of control signal and the performance was increased in the high-speed rapid lane change situation.

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Linear systems with multiple right-hand sides arise in many applications such as lattice quantum chromodynamics (QCD) calculation, the eigensolver using contour integral, and so on. Although the direct solvers are effective for solving the systems, it is difficult to apply them when the problem size is very large. Block Krylov subspace methods have been proposed as efficient numerical methods for solving the systems. In this paper, we describe the several Block Krylov subspace methods. After that, the cause of the deterioration of the accuracy of approximate solutions generated by the Block BiCGSTAB method is analyzed, and the Block BiCGGR method for computing high accuracy solutions is described.

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