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NUMERICAL ANALYSIS
Offering a clear, precise and accessible presentation, this book gives students the solid support they need to master basic numerical analysis techniques. It is suitable for a course in Numerical Methods for under-graduate students of all branches of engineering, students of Master of Computer Applications (MCA) and Bachelor of Computer Applications (BCA), and students pursuing diploma courses in engineering disciplines. The book can also serve as a useful reference for students of mathe-matics and statistics. The book focuses on core areas of numerical analysis such as errors in numerical computation, root finding, solution of algebraic equations, interpolation, numerical calculus, initial value problems, boundary value problems and eigenvalues. The underlying mathematical concepts are high-lighted through numerous worked-out examples. The section-end exercises contain plenty of problems with appropriate hints in order to motivate the students to work out problems for a deeper insight into subject concepts.
Biorthogonality and its Applications to Numerical Analysis
This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.
Foundations of Data Science
Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.
Software Systems for Structural Optimization
Herbert Hornlein, Klaus Schittkowski The finite element method (FEM) has been used successfully for many years to simulate and analyse mechanical structural problems. The results are accepted or rejected by means of comparison of state variables (stresses, displacements, natural frequencies etc.) and user requirements. In further analyses the design variables will be updated until the user specifications are met and the design is feasible. This is the primary aim of the design process. On this set of feasible designs, the additional requirement given by an objective function (e.g. weight, stiffness, efficiency, etc.) defines the structural optimization problem. In recent years more and more finite element based analysis systems were ex tended and offer now optimization modules. They proceed from the design model as defined for structural analysis, to perform an internal adaption of design pa rameters based on formal mathematical methods. Despite of many common features, there are significant differences in the selected optimization strategy, the current implementation and the numerical results.
Mathematics of Optimization: How to do Things Faster
Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the “why” and the “how” in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings.
Accuracy in Measurements and Calibrations, 1965
NBS estimates of uncertainties associated with physical measurements, and with some NBS calibration services, are shown by 66 provisional 'accuracy charts.'Each chart is accompanied by a facing page giving a brief statement of the state of the art and tentative plans for NBS * work in areas where improvement is needed. (Author).
13th Chaotic Modeling and Simulation International Conference
Gathering the proceedings of the 13th CHAOS2020 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.
Finite-Dimensional Linear Algebra
Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation. The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jord...
Static Analysis
Static analysis is increasingly recognized as a fundamental reasearch area aimed at studying and developing tools for high performance implementations and v- i cation systems for all programming language paradigms. The last two decades have witnessed substantial developments in this eld, ranging from theoretical frameworks to design, implementation, and application of analyzers in optim- ing compilers. Since 1994, SAS has been the annual conference and forum for researchers in all aspects of static analysis. This volume contains the proceedings of the 6th International Symposium on Static Analysis (SAS’99) which was held in Venice, Italy, on 22{24 September 1999. The previous SAS conferenc...
Soft Computing: Biomedical and Related Applications
This book lists current and potential biomedical uses of computational intelligence methods. These methods are used in diagnostics and treatment of such diseases as cancer, cardiac diseases, pneumonia, stroke, and COVID-19. Many biomedical problems are difficult; so, often, the current methods are not sufficient, new methods need to be developed. To confidently apply the new methods to critical life-and-death medical situations, it is important to first test these methods on less critical applications. The book describes several such promising new methods that have been tested on problems from agriculture, computer networks, economics and business, pavement engineering, politics, quantum computing, robotics, etc. This book helps practitioners and researchers to learn more about computational intelligence methods and their biomedical applications—and to further develop this important research direction.
