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Rank Deficient And Discrete Ill Posed Problems

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Rank Deficient And Discrete Ill Posed Problems

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Author : Per Christian Hansen
language : en
Publisher: SIAM
Release Date : 1998-01-01

Rank Deficient And Discrete Ill Posed Problems written by Per Christian Hansen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.

Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are either exactly or nearly rank deficient. Such problems often arise in connection with noise suppression and other problems where the goal is to suppress unwanted disturbances of the given measurements. Discrete ill-posed problems arise in connection with the numerical treatment of inverse problems, where one typically wants to compute information about some interior properties using exterior measurements. Examples of inverse problems are image restoration and tomography, where one needs to improve blurred images or reconstruct pictures from raw data. This book describes, in a common framework, new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed problems. The emphasis is on insight into the stabilizing properties of the algorithms and on the efficiency and reliability of the computations. The setting is that of numerical linear algebra rather than abstract functional analysis, and the theoretical development is complemented with numerical examples and figures that illustrate the features of the various algorithms.

Rank Deficient And Discrete Ill Posed Problems

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Author : Per Christian Hansen
language : en
Publisher: SIAM
Release Date : 2005-01-01

Rank Deficient And Discrete Ill Posed Problems

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Author : Per Christian Hansen
language : en
Publisher:
Release Date : 1996

Rank Deficient And Discrete Ill Posed Problems written by Per Christian Hansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Equations, Simultaneous categories.

Computation And Applied Mathematics

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Author :
language : en
Publisher:
Release Date : 2006

Computation And Applied Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Least Squares Data Fitting With Applications

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Author : Per Christian Hansen
language : en
Publisher: JHU Press
Release Date : 2013-01-15

Least Squares Data Fitting With Applications written by Per Christian Hansen and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-15 with Mathematics categories.

Included are; an overview of computational methods together with their properties and advantages; topics from statistical regression analysis that help readers to understand and evaluate the computed solutions; many examples that illustrate the techniques and algorithmsLeast Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.

Matrix Computations

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Author : Gene H. Golub
language : en
Publisher: JHU Press
Release Date : 2013-02-15

Matrix Computations written by Gene H. Golub and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-15 with Mathematics categories.

A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice. The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.

Practical Guide To Chemometrics

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Author : Paul Gemperline
language : en
Publisher: CRC Press
Release Date : 2006-04-16

Practical Guide To Chemometrics written by Paul Gemperline and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-16 with Mathematics categories.

The limited coverage of data analysis and statistics offered in most undergraduate and graduate analytical chemistry courses is usually focused on practical aspects of univariate methods. Drawing in real-world examples, Practical Guide to Chemometrics, Second Edition offers an accessible introduction to application-oriented multivariate meth

Fast Solution Of Discretized Optimization Problems

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Author : Karl-Heinz Hoffmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Fast Solution Of Discretized Optimization Problems written by Karl-Heinz Hoffmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Differential equations - partial as well as ordinary - are one of the main tools for the modeling of real world application problems. Pursuing the ultimate aim of influencing these systems in a desired way, one is confronted with the task of optimizing discretized models. This volume contains selected papers presented at the International Work shop on "Fast Solution of Discretized Optimization Problems", which took place at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin from May 08 until May 12, 2000. The conference was attended by 59 scientists from 10 countries. The scientific program consisted of 8 invited lectures presented by H. G. Bock (IWR Heidelberg) M. Heinkenschloss (Rice University, Houston) K. Kunisch (University of Graz) U. Langer (University Linz) B. Mohammadi (University of Montpellier) J. Petersson (University of Linkoping) E. Sachs (University of Trier) F. Troltzsch (Technical University of Chemnitz) and 28 contributed talks. The aim of this workshop was to foster the exchange of ideas between the still comparatively separated disciplines of nonlinear optimiza tion on the one side and numerical methods for differential equations on the other side. This is necessary for the successful solution of various current optimization problems in practical applications (shape optimization, topology optimization, pro cess optimization . . . ). Therefore the organizing committee as well as the speakers have come from both these communities.

Regularized Image Reconstruction In Parallel Mri With Matlab

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Author : Joseph Suresh Paul
language : en
Publisher: CRC Press
Release Date : 2019-11-05

Regularized Image Reconstruction In Parallel Mri With Matlab written by Joseph Suresh Paul and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Medical categories.

Regularization becomes an integral part of the reconstruction process in accelerated parallel magnetic resonance imaging (pMRI) due to the need for utilizing the most discriminative information in the form of parsimonious models to generate high quality images with reduced noise and artifacts. Apart from providing a detailed overview and implementation details of various pMRI reconstruction methods, Regularized image reconstruction in parallel MRI with MATLAB examples interprets regularized image reconstruction in pMRI as a means to effectively control the balance between two specific types of error signals to either improve the accuracy in estimation of missing samples, or speed up the estimation process. The first type corresponds to the modeling error between acquired and their estimated values. The second type arises due to the perturbation of k-space values in autocalibration methods or sparse approximation in the compressed sensing based reconstruction model. Features: Provides details for optimizing regularization parameters in each type of reconstruction. Presents comparison of regularization approaches for each type of pMRI reconstruction. Includes discussion of case studies using clinically acquired data. MATLAB codes are provided for each reconstruction type. Contains method-wise description of adapting regularization to optimize speed and accuracy. This book serves as a reference material for researchers and students involved in development of pMRI reconstruction methods. Industry practitioners concerned with how to apply regularization in pMRI reconstruction will find this book most useful.

Brain Source Localization Using Eeg Signal Analysis

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Author : Munsif Ali Jatoi
language : en
Publisher: CRC Press
Release Date : 2017-12-14

Brain Source Localization Using Eeg Signal Analysis written by Munsif Ali Jatoi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-14 with Science categories.

Of the research areas devoted to biomedical sciences, the study of the brain remains a field that continually attracts interest due to the vast range of people afflicted with debilitating brain disorders and those interested in ameliorating its effects. To discover the roots of maladies and grasp the dynamics of brain functions, researchers and practitioners often turn to a process known as brain source localization, which assists in determining the source of electromagnetic signals from the brain. Aiming to promote both treatments and understanding of brain ailments, ranging from epilepsy and depression to schizophrenia and Parkinson’s disease, the authors of this book provide a comprehensive account of current developments in the use of neuroimaging techniques for brain analysis. Their book addresses a wide array of topics, including EEG forward and inverse problems, the application of classical MNE, LORETA, Bayesian based MSP, and its modified version, M-MSP. Within the ten chapters that comprise this book, clinicians, researchers, and field experts concerned with the state of brain source localization will find a store of information that can assist them in the quest to enhance the quality of life for people living with brain disorders.

Rank Deficient And Discrete Ill Posed Problems

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