| In this dissertation, we've developed the procedures to get the Padé coefficients according to several methods. And we discuss in detail the characteristics of the denominator of Padé approximation schemes. We review the matrix techniques. If the matrix become a singular matrix, we are not able to approximate the real function with Padé approximation scheme. To prevent a matrix from being singular, we reduce the approximation range or change the orders of Padé approximation. In this dissertation, we apply newly developed Padé optimization techniques on the optimization areas and several numerical examples are examined to show the ability of Padé optimization techniques. Padé approximation schemes are also applied to computational mechanics areas including the eigenvalue problems of beams and plates, vibration problems, and mechanical design problems. The results are very accurate and good enough, when we compare these results to other methods. |
