Result: Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding: Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding
Title:
Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding: Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding
Authors:
Source:
SIAM Journal on Numerical Analysis. 40:1666-1682
Publisher Information:
Society for Industrial & Applied Mathematics (SIAM), 2002.
Publication Year:
2002
Subject Terms:
rootfinding, General theory of numerical methods in complex analysis (potential theory, etc.), transcendental equation, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), convert-to-powers, Computational aspects of field theory and polynomials, Numerical computation of solutions to single equations, zeros of nonpolynomial functions, degree-doubling, 0101 mathematics, 01 natural sciences, Chebyshev series
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1095-7170
0036-1429
0036-1429
DOI:
10.1137/s0036142901398325
Accession Number:
edsair.doi.dedup.....dab7cc2a8d8f334e7f54c67d8d2b922d
Database:
OpenAIRE
Further Information
Robust polynomial rootfinders are exploited to compute roots on a real interval of nonpolynomial function \(f(x)\) by (i) expanding \(f\) as a Chebyshev polynomial series, (ii) converting to a polynomial in ordinary form, and (iii) applying the polynomial rootfinder. Two conversion strategies are described:``convert-to-powers'' and ``degree-doubling''. Both strategies allow simultaneous approximation of many roots on an interval, whether simple or multiple.