Series: Classics in Applied Mathematics
Paperback (ISBN-13: 9780898716818)
This book is the definitive 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. 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.
* A true classic, this is the only systematic development of the theory
of matrix polynomials; nothing has come close for 20 years * Includes applications
to differential and difference equations * Written for a wide audience
of student and practising engineers, scientists, and mathematicians
Preface to the Classics Edition; Preface; Errata; Introduction; Part I.
Monic Matrix Polynomials: 1. Linearization and standard pairs; 2. Representation
of monic matrix polynomials; 3. Multiplication and divisibility; 4. Spectral
divisors and canonical factorization; 5. Perturbation and stability of
divisors; 6. Extension problems; Part II. Nonmonic Matrix Polynomials:
7. Spectral properties and representations; 8. Applications to differential
and difference equations; 9. Least common multiples and greatest common
divisors of matrix polynomials; Part III. Self-Adjoint Matrix Polynomials:
10. General theory; 11. Factorization of self-adjoint matrix polynomials;
12. Further analysis of the sign characteristic; 13: Quadratic self-adjoint
polynomials; Part IV. Supplementary Chapters in Linear Algebra: S1. The
Smith form and related problems; S2. The matrix equation AX * XB = C; S3.
One-sided and generalized inverses; S4. Stable invariant subspaces; S5.
Indefinite scalar product spaces; S6. Analytic matrix functions; References;
List of notation and conventions; Index.
Paperback (ISBN-13: 9780898716764)
The purpose of this book is to promote understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. Sensitivity and stability are analyzed as mathematical properties, without reference to finite precision arithmetic. The material is presented at a basic level, emphasizing ideas and intuition, but in a mathematically rigorous fashion. The derivations are simple and elegant, and the results are easy to understand and interpret. The book is self-contained. It was written for students in all areas of mathematics, engineering, and the computational sciences, but can easily be used for self-study. This text differs from other numerical linear algebra texts by offering the following: a systematic development of numerical conditioning; a simplified concept of numerical stability in exact arithmetic; simple derivations; a high-level view of algorithms; and results for complex matrices.
* The material is presented at a basic level, emphasising ideas and intuition
* Each chapter offers simple exercises for use in the classroom and more
challenging exercises for student practice * Written for advanced undergraduates
and graduates in mathematics, engineering and computational science
Preface; Introduction; 1. Matrices; 2. Sensitivity, errors, and norms; 3. Linear systems; 4. Singular value decomposition; 5. Least square problems; 6. Subspaces; Index.
Paperback (ISBN-13: 9780521118446)
Michael Powell is one of the world’s foremost figures in numerical analysis. This volume, first published in 1997, is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell’s own achievements, focuses on innovative work in optimisation and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys. They have all been reviewed and edited to form a coherent volume for this important discipline within mathematics, with highly relevant applications throughout science and engineering.
* Highly relevant research results in numerical mathematics * Subjects
include two of the most important applications of numerical analysis *
Authors of papers are carefully chosen experts in those fields
Preface; Submitted talks; 1. M. J. D. Powell's contributions to numerical mathematics M. D. Buhmann and R. Fletcher; 2. MJDP-BCS industrial liaison: applications to defence science I. Barrodale and C. Zala; 3. On the Meir/Sharma/Hall/Meyer analysis of the spline interpolation error C. de Boor; 4. Asymptotically optimal approximation and numerical solutions of differential equations M. D. Buhmann, C. A. Micchelli and A. Ron; 5. On the convergence of derivative-free methods for unconstrained optimization A. R. Conn, K. Scheinberg and Ph. L. Toint; 6. Least squares fitting to univariate data subject to restrictions on the signs of the second differences I. C. Demetriou and M. J. D. Powell; 7. A framework for interpolation and approximation on Riemannian manifolds N. Dyn, F. J. Narcowich and J. D. Ward; 8. Dense factors of sparse matrices R. Fletcher; 9. Optimization environments and the NEOS Server W. Gropp and J. J. More; 10. New versions of qd for products of bidiagonals B. N. Parlett; 11. On adjusting parameters in homotopy methods for linear programming M. J. Todd.
Details
Page extent: 340 pages
Size: 216 x 140 mm
Weight: 0.43 kg
Paperback (ISBN-13: 9780521098717)
This book was intended as a first course in coordinate geometry of the type envisaged in the Report on the Teaching of Higher Geometry in schools, prepared for the Mathematical Association in 1953. There is however sufficient material to also meet the needs of those reading for a general degree including mathematics. The focus is on Cartesian plane, but with introductory material to the algebra, trigonometry and calculus needed.
Preface; 1. The Point; 2. The Line; 3. The Parabola; 4. Curves Defined
Parametrically; 5. The Circle; 6. The Ellipse and Hyperbola; 7. Line Pairs;
8. The General Conic; 9. Polar Coordinates; 10. What is a Conic*; Further
miscellaneous Examples; Formulae for Reference; Hints on the Solution of
Examples; Answers to Examples; Index.
Series: Classics in Applied Mathematics
Paperback (ISBN-13: 9780898716788)
Polynomial continuation is a numerical technique used to compute solutions to systems of polynomial equations. Originally published in 1987, this introduction to polynomial continuation remains a useful starting point for the reader interested in learning how to solve practical problems without advanced mathematics. Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems is easy to understand, requiring only a knowledge of undergraduate-level calculus and simple computer programming. The book is also practical; it includes descriptions of various industrial-strength engineering applications and offers Fortran code for polynomial solvers on an associated Web page. It provides a resource for undergraduate mathematics projects.
* Elementary and easy to understand - its prerequisites are only advanced
calculus and simple computer programming * Includes Fortran code for polynomial
solvers that are powerful enough to be useful but simple enough to translate
into other computer languages * A classic which was first published in
1987, yet still remains up-to-date
Preface to the classics edition; Preface; Introduction; Part I. The Method: 1. One equation in one unknown; 2. Two equations in two unknowns; 3. General systems; 4. Implementation; 5. Scaling; 6. Other continuation methods; Part II. Applying the Method: 7. Reduction; 8. Geometric intersection problems; 9. Chemical equilibrium systems; 10. Kinematics of mechanisms; Appendices: Appendix 1. Newton's method; Appendix 2. Emulating complex operations in real arithmetic; Appendix 3. Some real-complex calculus formulas; Appendix 4. Proofs of results from Chapter 3; Appendix 5. Gaussian elimination for system reduction; Appendix 6. Computer programs; Bibliographies and References: Brief bibliography; Addition bibliography; References; Index.