Programs in Physics & Physical Chemistry
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|Manuscript Title: Subroutine for calculation of matrix Pade approximants.|
|Authors: Y. Starkand|
|Program title: PADE APPROXIMANTS|
|Catalogue identifier: ACWV_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 11(1976)325|
|Programming language: Fortran.|
|Computer: IBM 370/165.|
|Operating system: OS360.|
|RAM: 63K words|
|Word size: 32|
|Keywords: General purpose, Pade Approximant, Perturbation series, Expansion coefficients.|
Nature of problem:
This computer program contains subroutines which calculate any desired Pade approximant. Given the appropriate number of coefficients in the perturbation expansion of a matrix-valued function of any given dimension, the program computes the approximant at a given point x.
Calculations are done in double-precision mode (each number occupies two 32-bit words in memory). All the quantities calculated are kept in the active area. If matrices of large dimensions are to be used or approximants of high order calculated, the program could be easily modified to keep most of the information on tape or disk to reduce memory use.
Running time depends roughly on the square of the order of the matrices involved and on the square of the order of the approximant requested. To give an order of magnitude for the running time we mention that calculating the [6,5] Pade approximant for a three by three-dimensional problem needed 0.9 s on an IBM 370/165. The test program enclosed needed 4.63 s for calculating 66 pade approximants ranging from [1,1] to [11,7] pade approximant.
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