Advances in Numerical Analysis Emphasizing with Interval Data

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Advances in Numerical Analysis Emphasizing with Interval Data by Tofigh Allahviranloo

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Numerical analysis is the cornerstone of computations in numerical methods, especially recently, interval numerical calculations play an important role in all topics of engineering and physical sciences and even in life sciences, social sciences, medicine, business, and art. The recent growth in computational potency has made it possible to use more sophisticated numerical analysis and to provide accurate and realistic mathematical models in the sciences. Researchers’ interest in computing uncertain data, that is, interval data, opens up new avenues for tackling real-world problems and offers innovative and efficient solutions.


This book provides the basic theoretical foundations of numerical methods, discusses classes of key techniques, explains their advances, and provides insights into recent developments and challenges. The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the first feature of the book is an up-to-date and focused dissertation on computational error analysis, in particular a comprehensive and systematic treatment of error propagation mechanisms. The second one is considerations on the quality of data related to numerical calculations with a full discussion of distance approximation theory. The third feature focuses on the theory of approximation and its development from the perspective of linear algebra. Finally, the new and regular view of numerical integration and their solutions enhanced by error analysis is presented as the last feature of the book.


The book will be of interest to the broad spectrum of readers exploring interval computing in numerical analysis. It could be also of particular interest to graduate students in engineering and applied mathematics.


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