An efficient algorithm for partial fraction expansion of the linear matrix pencil inverse |
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| Institution: | 1. Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023;2. Key Laboratory of Dark Matter and Space Astronomy, Chinese Academy of Sciences, Nanjing 210023;3. University of Chinese Academy of Sciences, Beijing 100049;1. Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt;2. Department of Mathematics and Actuarial Science, The American University in Cairo, Cairo, Egypt;1. School of Science, Tianjin Polytechnic University, Tianjin 300378, China;2. Henan Costar Group Co., Ltd, Henan 473000, China |
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| Abstract: | A new algorithm for computations of matrix partial fractions representing the inverse of linear matrix pencil is based on an appropriate expression in matrix form of the Pascal triangle. It concerns singular and nonsingular systems and starts with the inverse of regular matrix linear pencil M(s) = sA0 - A where only A0 is singular, or both A0 and A are singular. Nonsingular systems are considered as a particular case of singular systems. The presented algorithm of the matrix partial fraction expansion is suitable to determine the matrix transfer function, and is computer oriented because all manipulations can be performed on matrices with constant entries only. |
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