Loading...
Please wait, while we are loading the content...
Similar Documents
Partial fraction evaluation and incomplete decomposition of a rational function whose denominator contains a repeated polynomial factor
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mahoney, John F. |
| Copyright Year | 1985 |
| Abstract | Attention is directed to those proper rational functions whose denominators may be expressed as the product of an Nth degree polynomial raised to the Kth power and another polynomial of degree M. A method is presented for decomposing such a rational function into the sum of the K partial fraction terms which proceed from the repeated polynomial plus a proper rational function which completes the equality. Use is made of an extended version of Homer's scheme. Two numerical examples and an operations count are presented. The method is free of complex arithmetic provided that all of the coefficients of the entering polynomials are real. Introduction. Consider the proper rational function (1) F(s) = -KB (s) QK(S )A(s)' where Q(s) is a polynomial of degree N (N > 1), A(s) is a polynomial of degree M which shares none of its zeros with Q(s); B(s) is a polynomial of degree m (m 1 by writing QK(S) as Q(s), which has the effect of redacing the problem to the K = 1 case. For this problem one may find C1(s) which, in Lurn, by repeated use of long division, may be written as CI(s) + C2(s)Q(s) + _K* S -F C(s)QK(s). Subsequent division by QK(S) gives the summation portion of (2). Received March 8, 1983; revised November 16, 1983 and February 10, 1984. 1980 Mathematics Subject Classification. Primary 65F99. ?1985 American Mathematical Society 0025-5718/85 $1.00 + $.25 per page 167 This content downloaded from 157.55.39.58 on Tue, 11 Oct 2016 04:48:47 UTC All use subject to http://about.jstor.org/terms |
| Starting Page | 167 |
| Ending Page | 175 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0025-5718-1985-0771038-X |
| Volume Number | 44 |
| Alternate Webpage(s) | http://www.ams.org/journals/mcom/1985-44-169/S0025-5718-1985-0771038-X/S0025-5718-1985-0771038-X.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0025-5718-1985-0771038-X |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
