Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.

This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals

The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.

An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.

A comprehensive guide to the design and execution of sophisticated exterior building enclosures Focused on the design process for architects and related professionals, this book addresses the design and execution of sophisticated exterior building enclosures for a number of commercial building types and in a variety of building materials. It focuses on the design process by delineating enclosure basics, the participants (owners, architects, engineers, consultants) and their roles and responsibilities through collaboration, and tracking the design process through construction. This comprehensive handbook covers all of the factors that affect the design of a building enclosure, including function, visual aesthetics, performance requirements, and many other criteria. In-depth case studies of projects of various scales, types, and climate conditions illustrate the successful implementation of exterior wall enclosure solutions in brick masonry, stone, architectural concrete, glass, and metals. This unique and indispensable guide: Defines the functions, physical requirements, design principles, and types of exterior building enclosures Identifies the participants in the design and construction process and specifies their roles and responsibilities Presents a step-by-step process for the design of exterior enclosures, from defining goals and developing concepts through creating construction documents Reviews the construction process from bidding and negotiation through the paper phase to the "brick and mortar" stage Provides details on the properties of exterior enclosure materials, including structural considerations, weather protection, fire safety, and more Covers a variety of materials, including brick masonry, natural stone masonry, architectural concrete, metal framing and glass, and all-glass enclosures Written by the technical director of the San Francisco office of Skidmore, Owings & Merrill, Exterior Building Enclosures is an indispensable resource for architects, engineers, facade consultants, and green design consultants working on commercial building projects.

The aim of this volume is to present an overview of current trends and individual methodological attempts towards arriving at an adequate understanding of Minoan, Cycladic, and Mycenaean iconography.

To describe the true behavior of most real-world systems with sufficient accuracy, engineers have to overcome difficulties arising from their lack of knowledge about certain parts of a process or from the impossibility of characterizing it with absolute certainty. Depending on the application at hand, uncertainties in modeling and measurements can be represented in different ways. For example, bounded uncertainties can be described by intervals, affine forms or general polynomial enclosures such as Taylor models, whereas stochastic uncertainties can be characterized in the form of a distribution described, for example, by the mean value, the standard deviation and higher-order moments. The goal of this Special Volume on Modeling, Design, and Simulation of Systems with Uncertainties is to cover modern methods for dealing with the challenges presented by imprecise or unavailable information. All contributions tackle the topic from the point of view of control, state and parameter estimation, optimization and simulation. Thematically, this volume can be divided into two parts. In the first we present works highlighting the theoretic background and current research on algorithmic approaches in the field of uncertainty handling, together with their reliable software implementation. The second part is concerned with real-life application scenarios from various areas including but not limited to mechatronics, robotics, and biomedical engineering.