Recent and ongoing improvements in computer technology have increased the need for efficient and reliable design tools; computational methods have opened the door to making sensitivity analysis a tractable design tool...
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ISBN:
(数字)9780898717556
ISBN:
(纸本)9780898715248
Recent and ongoing improvements in computer technology have increased the need for efficient and reliable design tools; computational methods have opened the door to making sensitivity analysis a tractable design tool for industries that design and manufacture high performance products. These industries are increasingly interested in exploiting the advantages of computer-aided design, numerical analysis, and optimal design methods. This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations.
frontiers in applied mathematics Inverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting. This book provides the reader with a basic understandin...
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ISBN:
(数字)9780898717570
ISBN:
(纸本)9780898715071
frontiers in applied mathematics
Inverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting. This book provides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics like image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods.
Because inverse problems typically involve the estimation of certain quantities based on indirect measurements, the estimation process is often ill-posed. Regularization methods, which have been developed to deal with this ill-posedness, are carefully explained in the early chapters of Computational Methods for Inverse Problems. The book also integrates mathematical and statistical theory with applications and practical computational methods, including topics like maximum likelihood estimation and Bayesian estimation.
Several web-based resources are available to make this monograph interactive, including a collection of MATLAB m-files used to generate many of the examples and figures. These resources enable readers to conduct their own computational experiments in order to gain insight. They also provide templates for the implementation of regularization methods and numerical solution techniques for other inverse problems. Moreover, they include some realistic test problems to be used to further develop and test various numerical methods.
This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of math...
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ISBN:
(数字)9780898717594
ISBN:
(纸本)9780898714753
This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.
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