An analogue for Szegő polynomials of the Clenshaw algorithm
✍ Scribed by Gregory S. Ammar; William B. Gragg; Lothar Reichel
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 368 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0377-0427
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We discuss an iterative algorithm that approximates all roots of a univariate polynomial. The iteration is based on floating-point computation of the eigenvalues of a generalized companion matrix. With some assumptions, we show that the algorithm approximates the roots within about log ρ/ χ(P ) iter
Gilmer and Heinzer proved that given a reduced ring R, a polynomial f divides a monic polynomial in R[X] if and only if there exists a direct sum decomposition of R = R0 ⊕ . . . ⊕ Rm (m ≤ deg f ), associated to a fundamental system of idempotents e0, . . . , em, such that the component of f in each