Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté. Image fixe : sans médiation
Auteur(s) : Boyd, John P. (1951-....)
Titre(s) : Solving transcendental equations [Texte imprimé] : the Chebyshev polynomial proxy and other numerical rootfinders, perturbation series, and oracles / John P. Boyd,...
Publication : Philadelphia : Society for Industrial and applied mathematics, cop. 2014
Description matérielle : 1 vol. (XVIII-460 p.) : ill. ; 26 cm
Comprend : I: Introduction and overview ; Introduction: Key themes in rootfinding ; II: the
Chebyshev-Proxy rootfinder and its generalizations ; The Chebyshev-Proxy/Companion
matrix rootfinder ; Adaptive Chebyshev interpolation ; Adaptive Fourier interpolation
and rootfinding ; Complex zeros: Interpolation on a disk, the Delves-Lyness algorithm,
and contour integrals ; III: Fundamentals: Interations, bifurcation, and continuation
; Newton iteration and its kin ; Bifurcation theory ; Continuation in a parameter
; IV: Polynomials ; Polynomial equations and the irony of Galois Theory ; The Quadratic
Equation ; Roots of a cubic polynomial ; Roots of a quartic polynomial ; V: Analytical
methods ; Methods for explicit solutions ; Regular perturbation methods for roots
; Singular perturbation methods: fractional powers, logarithms, and exponential asympototics
; VI: Classics, special functions, inverses, and oracles ; Classical methods for
solving one equation in one unknown ; Special algorithms for special functions ;
Inverse functions of one unknown ; Oracles: Theorems and algorithms for determining
the existence, nonexistence, and number of zeros ; VII: Bivariate systems ; Two
equations in two unknowns ; VIII: Challenges ; Past and future ; A: Companion matrices
; B: Chebyshev interpolation and quadrature ; Marching triangles ; D: Imbricate-Fourier
series and the Poisson Summation Theorem.
Note(s) : Bibliogr. p. 433-454
Sujet(s) : Fonctions transcendantes
Nombres transcendants
Tchebychev, Polynômes de
Indice(s) Dewey :
515.22 (23e éd.) = Propriétés des fonctions (mathématiques)
Identifiants, prix et caractéristiques : ISBN 9781611973518. - ISBN 1611973511 (br.)
Identifiant de la notice : ark:/12148/cb439016579
Notice n° :
FRBNF43901657
(notice reprise d'un réservoir extérieur)
