کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4639771 | 1341250 | 2012 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A fitting algorithm for real coefficient polynomial rooting A fitting algorithm for real coefficient polynomial rooting](/preview/png/4639771.png)
A new algorithm for computing all roots of polynomials with real coefficients is introduced. The principle behind the new algorithm is a fitting of the convolution of two subsequences onto a given polynomial coefficient sequence. This concept is used in the initial stage of the algorithm for a recursive slicing of a given polynomial into degree-2 subpolynomials from which initial root estimates are computed in closed form. This concept is further used in a post-fitting stage where the initial root estimates are refined to high numerical accuracy. A reduction of absolute root errors by a factor of 100 compared to the famous Companion matrix eigenvalue method based on the unsymmetric QR algorithm is not uncommon. Detailed computer experiments validate our claims.
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 13, July 2012, Pages 3238–3255