✦ LIBER ✦

The amended DSeSC power method for polynomial root-finding

✍ Scribed by V.Y. Pan

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 724 KB
Volume: 49
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2004.09.011

No coin nor oath required. For personal study only.

✦ Synopsis

Cardinal's matrix version of the Sebastiao e Silva polynomial root-finder rapidly approximates the roots as the eigenvalues of the associated Frobenius matrix. We preserve rapid convergence to the roots but amend the algorithm to allow input polynomials with multiple roots and root clusters. As in Cardinal's algorithm, we repeatedly square the Frobenius matrix in nearly linear arithmetic time per squaring, which yields dramatic speedup versus the recent effective polynomial root-finder based on the application of the inverse power method to the F~obenius matrix.

📜 SIMILAR VOLUMES

Method for finding multiple roots of pol

Method for finding multiple roots of polynomials

✍ Chang-Dau Yan; Wei-Hua Chieng 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 851 KB

Conventional numerical methods for finding multiple roots of polynomials are inaccurate. The accuracy is unsatisfactory because the derivatives of the polynomial in the intermediate steps of the associated root-finding procedures are eliminated. Engineering applications require that this problem be

Numerical integration error method – a n

Numerical integration error method – a new method for polynomial root-finding

✍ Tomohiro Suzuki; Toshio Suzuki 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 294 KB

A method of finding the roots of polynom

A method of finding the roots of polynomials which converge for any initial approximation

✍ A.V. Ivanisov; V.K. Polishchuk 📂 Article 📅 1985 🏛 Elsevier Science ⚖ 674 KB

An approximate method of finding the gre

An approximate method of finding the greatest of the moduli of the roots of a polynomial

✍ S.A. Ivanov; A.Ya. Lepin; E.I. Lepina 📂 Article 📅 1976 🏛 Elsevier Science ⚖ 111 KB

An iterative method for finding a simple

An iterative method for finding a simple root of the equation f(x) = 0

✍ R. Krautstengl 📂 Article 📅 1968 🏛 Elsevier Science ⚖ 234 KB

A note on the convergence of the Weierst

A note on the convergence of the Weierstrass sor method for polynomial roots

✍ M.S. Petković; N. Kjurkchiev 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 428 KB

Convergence properties of the SOR Weierstrass method for the simultaneous approximation of polynomial roots are considered. The choice of acceleration parameter is discussed.