Browsing by Subject "Diagonalization"
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Item Open Access Error control in MLFMA with multiple-precision arithmetic(Institution of Engineering and Technology, 2018-04) Kalfa, Mert; Ergül, Ö.; Ertürk, Vakur B.We present a new error control method that provides the truncation numbers as well as the required digits of machine precision for the translation operator of the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems (i.e., electrically large translation distances). When combined with a multiple-precision implementation of MLFMA, the proposed method can be used to solve low-frequency problems that are problematic with a fixed-precision implementation. Numerical results in the form of optimal truncation numbers and machine precisions for a variety of box sizes and desired relative error thresholds are presented and compared with the methods or numerical surveys available in the literature.Item Open Access Error control of multiple-precision MLFMA(Institute of Electrical and Electronics Engineers, 2018) Kalfa, M.; Ergül, Ö.; Ertürk, VakurWe introduce and demonstrate a new error control scheme for the computation of far-zone interactions in the multilevel fast multipole algorithm when implemented within a multiple-precision arithmetic framework. The proposed scheme provides the optimum truncation numbers as well as the machine precisions given the desired relative error thresholds and the box sizes for the translation operator at all frequencies. In other words, unlike the previous error control schemes which are valid only for high-frequency problems, the proposed scheme can be used to control the error across both low- A nd high-frequency problems. Optimum truncation numbers and machine precisions are calculated for a wide range of box sizes and desired relative error thresholds with the proposed error control scheme. The results are compared with the previously available methods and numerical surveys.Item Open Access On diagonalization by dynamic output feedback(1989) Özgüler, A. B.; Eldem, V.The purpose of this paper is to draw attention to a casuality degree dominance property in diagonalization problems by dynamic output feedback and constant precompensator. Even in the well-investigated special case of square transfer matrices, the property of degree-dominance yields new insight into the structure of diagonalizable transfer matrices.