Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

This chapter treats several topics, starting with Bernoulli’s method. This method iteratively solves a linear difference equation whose coefficients are the same as those of the polynomial. The ratios of successive iterates tends to the root of largest magnitude. Special versions are used for complex and/or multiple roots. The iteration may be accelerated, and Aitken’s variation finds all the roots simultaneously. The Quotient-Difference algorithm uses two sequences(with a similar one for ). Then, if the roots are well separated, . Special techniques are used for roots of equal modulus. The Lehmer–Schur method uses a test to determine whether a given circle contains a root or not. Using this test we find an annulus which contains a root, whereas the circle does not. We cover the annulus with 8 smaller circles and test which one contains the roots. We repeat the process until a sufficiently small circle is known to contain the root. We also consider methods using integration, such as by Delves–Lyness and Kravanja et al.

This book constitutes the proceedings of the 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, held in Beijing, China, in September 2017. The 28 full papers presented in this volume were carefully reviewed and selected from 33 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.

Towards the end of the 1960s, a number of quite different circumstances combined to launch a period of intense activity in the digital processing of electron micro graphs. First, many years of work on correcting the resolution-limiting aberrations of electron microscope objectives had shown that these optical impediments to very high resolution could indeed be overcome, but only at the cost of immense exper imental difficulty; thanks largely to the theoretical work of K. -J. Hanszen and his colleagues and to the experimental work of F. Thon, the notions of transfer func tions were beginning to supplant or complement the concepts of geometrical optics in electron optical thinking; and finally, large fast computers, capable of manipu lating big image matrices in a reasonable time, were widely accessible. Thus the idea that recorded electron microscope images could be improved in some way or rendered more informative by subsequent computer processing gradually gained ground. At first, most effort was concentrated on three-dimensional reconstruction, particu larly of specimens with natural symmetry that could be exploited, and on linear operations on weakly scattering specimens (Chap. l). In 1973, however, R. W. Gerchberg and W. O. Saxton described an iterative algorithm that in principle yielded the phase and amplitude of the electron wave emerging from a strongly scattering speci men.

Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms. The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence. The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions. The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.

Sifting through the variety of control systems applications can be a chore. Diverse and numerous technologies inspire applications ranging from float valves to microprocessors. Relevant to any system you might use, the highly adaptable Control System Fundamentals fills your need for a comprehensive treatment of the basic principles of control system engineering. This overview furnishes the underpinnings of modern control systems. Beginning with a review of the required mathematics, major subsections cover digital control and modeling. An international panel of experts discusses the specification of control systems, techniques for dealing with the most common and important control system nonlinearities, and digital implementation of control systems, with complete references. This framework yields a primary resource that is also capable of directing you to more detailed articles and books. This self-contained reference explores the universal aspects of control that you need for any application. Reliable, up-to-date, and versatile, Control System Fundamentals answers your basic control systems questions and acts as an ideal starting point for approaching any control problem.

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Theory and Phenomena of Metamaterials offers an in-depth look at the theoretical background and basic properties of electromagnetic artificial materials, often called metamaterials. A volume in the Metamaterials Handbook, this book provides a comprehensive guide to working with metamaterials using topics presented in a concise review format along with numerous references. With contributions from leading researchers, this text covers all areas where artificial materials have been developed. Each chapter in the text features a concluding summary as well as various cross references to address a wide range of disciplines in a single volume.