Computing real roots of a polynomial in Chebyshev series form through subdivision

• Published in: Applied numerical mathematics Vol. 56; no. 8; pp. 1077 - 1091
• Main Author: Boyd, John P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2006; Elsevier
• Subjects: Algebra; Chebyshev polynomials; Exact sciences and technology; Field theory and polynomials; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Rootfinding; Sciences and techniques of general use; Rootfinding; Chebyshev polynomials; Numerical analysis; Error estimation; Partition method; Applied mathematics; Chebyshev polynomial; Approximation error; Matrix method; Computing; Algorithm

An arbitrary polynomial of degree N, f N ( x ) , can always be represented as a truncated Chebyshev polynomial series (“Chebyshev form”). This representation is much better conditioned than the usual “power form” of a polynomial. We describe two families of algorithms for finding the real roots of f...