polynomial

Teaching Systems Algebra Module 7: Polynomials
$49.98
Polynomials, standard form, leading coeffi cient, constant term, factor, quotient, and even & odd degrees.

Number Theory and Polynomials (London Mathematical Society Lecture Note Series)
$70.00
Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of number-theoretic interests, and the book's contents reflect the quality of the meeting. Topics covered include recent work on the Schur-Siegel-Smyth trace problem, Mahler measure and its generalisations, the merit factor problem, Barker sequences, K3-surfaces, self-inversive polynomials, Newman's inequality, algorithms for sparse polynomials, the integer transfinite diameter, divisors of polynomials, non-linear recurrence sequences, polynomial ergodic averages, and the Hansen-Mullen primitivity conjecture. With surveys and expository articles presenting the latest research, this volume is essential for graduates and researchers looking for a snapshot of current progress in polynomials and number theory.

Polynomial Root-finding and Polynomiography
$93.00
This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations. Contents: Approximation of Square-Roots and Their Visualizations; The Fundamental Theorem of Algebra and a Special Case of Taylor s Theorem; Introduction to the Basic Family and Polynomiography; Equivalent Formulations of the Basic Family; Basic Family as Dynamical System; Fixed Points of the Basic Family; Algebraic Derivation of the Basic Family and Characterizations; The Truncated Basic Family and the Case of Halley Family; Characterizations of Solutions of Homogeneous Linear Recurrence Relations; Generalization of Taylor s Theorem and Newton s Method; The Multipoint Basic Family and Its Order of Convergence; A Computational Study of the Multipoint Basic Family; A General Determinantal Lower Bound; Formulas for Approximation of Pi Based on Root-Finding Algorithms; Bounds on Roots of Polynomials and Analytic Functions; A Geometric Optimization and Its Algebraic Offsprings; Polynomiography: Algorithms for Visualization of Polynomial Equations; Visualization of Homogeneous Linear Recurrence Relations; Applications of Polynomiography in Art, Education, Science and Mathematics; Approximation of Square-Roots Revisited; Further Applications and Extensions of the Basic Family and Polynomiography.

Matrix Polynomials (Classics in Applied Mathematics)
$92.00
This book provides a comprehensive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the Wiener Hopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. Audience: The book is appropriate for students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex analysis. Contents: Preface to the Classics Edition; Preface; Errata; Introduction; Part I: Monic Matrix Polynomials: Chapter 1: Linearization and Standard Pairs; Chapter 2: Representation of Monic Matrix Polynomials; Chapter 3: Multiplication and Divisability; Chapter 4: Spectral Divisors and Canonical Factorization; Chapter 5: Perturbation and Stability of Divisors; Chapter 6: Extension Problems; Part II: Nonmonic Matrix Polynomials: Chapter 7: Spectral Properties and Representations; Chapter 8: Applications to Differential and Difference Equations; Chapter 9: Least Common Multiples and Greatest Common Divisors of Matrix Polynomials; Part III: Self-Adjoint Matrix Polynomials: Chapter 10: General Theory; Chapter 11: Factorization of Self-Adjoint Matrix Polynomials; Chapter 12: Further Analysis of the Sign Characteristic; Chapter 13: Quadratic Self-Adjoint Polynomials; Part IV: Supplementary Chapters in Linear Algebra: Chapter S1: The Smith Form and Related Problems; Chapter S2: The Matrix Equation AX XB = C; Chapter S3: One-Sided and Generalized Inverses; Chapter S4: Stable Invariant Subspaces; Chapter S5: Indefinite Scalar Product Spaces; Chapter S6: Analytic Matrix Functions; References; List of Notation and Conventions; Index