SBN: 978-0-471-20170-0
Hardcover
360 pages
March 2008
The EM Algorithm and Extensions remains the only single source to offer a complete and unified treatment of the theory, methodology, and applications of the EM algorithm. The highly applied area of statistics here outlined involves applications in regression, medical imaging, finite mixture analysis, robust statistical modeling, survival analysis, and repeated-measures designs, among other areas. The text includes newly added and updated results on convergence, and new discussion of categorical data, numerical differentiation, and variants of the EM algorithm. It also explores the relationship between the EM algorithm and the Gibbs sampler and Markov Chain Monte Carlo methods.
ISBN: 978-0-470-08501-1
Hardcover
392 pages
April 2008
Finally there's an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems. With this approach, they'll gain a strong understanding of the mathematical language as they discover how to apply it in order to find proofs.
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science Volume: 15
ISBN: 9781584885795
Publication Date: 3/26/2008
Number of Pages: 488
Presents techniques, such as transform methods and Greenfs function, necessary to solve difficult problems found in many scientific and engineering areas, including elasticity and biomechanics
Organizes examples of problems by the type of dual or triple integral equation
Discusses the history of mixed boundary value problems
Uses MATLAB to illustrate the solutions
Contains MATLAB code so readers can reproduce some of the examples
Methods for Solving Mixed Boundary Value Problems
An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations.
Straightforward Presentation of Mathematical Techniques
The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve various mixed boundary value problems using separation of variables, transform methods, the Wiener?Hopf technique, Greenfs function, and conformal mapping.
Decipher Mixed Boundary Value Problems That Occur in Diverse Fields
ISBN: 9781420063639
Publication Date: 3/19/2008
Number of Pages: 424
Explores the basics of Fourier analysis, which connects the DFT to the continuous Fourier transform, the Fourier series, and the sampling theorem
Provides numerous graphical illustrations and worked examples supported by numerical results using MATLABR
Explains the DFT of windowed sequences, the working of various discrete convolution algorithms, and their applications in digital filtering and filters through examples and diagrams
Covers the mathematical background and implementation-related issues of prime factor FFT algorithms
Discusses the array-smart implementation of the FFT algorithm for computing the DFT of arbitrary (possibly prime) length
Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms presents the fundamentals of Fourier analysis and their deployment in signal processing using DFT and FFT algorithms.
This accessible, self-contained book provides meaningful interpretations of essential formulas in the context of applications, building a solid foundation for the application of Fourier analysis in the many diverging and continuously evolving areas in digital signal processing enterprises. It comprehensively covers the DFT of windowed sequences, various discrete convolution algorithms and their applications in digital filtering and filters, and many FFT algorithms unified under the frameworks of mixed-radix FFTs and prime factor FFTs. A large number of graphical illustrations and worked examples help explain the concepts and relationships from the very beginning of the text.
Requiring no prior knowledge of Fourier analysis or signal processing, this book supplies the basis for using FFT algorithms to compute the DFT in a variety of application areas.