Mathematica for Scientists and Engineers

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Ee-Leng Tan, Woon-Seng Gan

This book first introduces classic as well as recent computational models for just-noticeable-difference (JND) applications. Since the discrete cosine transform (DCT) is applied in many image and video standards (JPEG, MPEG-1/2/4, H.261/3), the book also includes a comprehensive survey of computational models for JND that are based on DCT. The visual factors used in these computational models are reviewed in detail. Further, an extensive comparative analysis of these models using quantitative and qualitative performance criteria is presented, which compares the noise shaping performance of these models with subjective evaluation and the accuracy between the estimated JND thresholds and subjective evaluation. There are many surveys available on computational models for JND; however, these surveys seldom compare the performance of computational models that are based on DCT. The authors? survey of the computational models and their in-depth review of the visual factors used in them will help readers understand perceptual image coding based on DCT. The book also provides a comparative analysis of several perceptual image coders that are based on DCT, which are compatible with the highly popular and widely adopted JPEG standard.

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Dietmar Hildenbrand

<p>The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics.</p><p><p>This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications.</p><p>The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

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Sadri Hassani

"This book presents a large number of numerical topics and exercises together with discussions of methods for solving such problems using Mathematica. The accompanying CD-ROM contains Mathematica Notebooks for illustrating most of the topics in the text and for solving problems in mathematical physics." "Although is it primarily designed for use with the author's Mathematical Methods: For Students of Physics and Related Fields, the discussions in the book are sufficiently self-contained that the book can be used as a supplement to any of the standard textbooks in mathematical methods for undergraduate students of physical sciences or engineering."--Jacket.

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Tibor Csendes

The present volume contains 30 articles presented at SCAN-98, Budapest, Hungary. These papers cover all aspects of validation techniques in scientific computing, ranging from hardware requirements, elementary operations, high accuracy function evaluations and interval arithmetic to advanced validating techniques and applications in various fields of practical interest. Audience: This book is of interest to researchers and graduate students whose work involves validation techniques in scientific computing.