| Description |
1 online resource (vi, 195 pages) : illustrations (some color) |
| Contents |
01 Cover Page and Dedication.pdf; 02 Content; 03 Foreword; 04 Preface; 05 Contributors; 06 Chapter 1; Chapter 1. Exponential data fitting; 1.1. Introduction; Acknowledgement; 1.2. Solving separable nonlinear least squares problems with variable projections; 1.3. Complex VARPRO; 1.4. Prony-type or polynomial methods; 1.5. Subspace or matrix-pencil method HTLS/HSVD; 1.6. Numerical results; 1.7. Some applications; 1.8. Appendix; Bibliography; Chapter 2. Computational aspects of exponential data fitting in Magnetic Resonance Spectroscopy; 2.1. Introduction |
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2.2. The classical exponential model for MRS signals2.3. The model for short echo time MRS signals; 2.4. Model distortions and preprocessing methods; 2.5. Conclusions; Appendix; Acknowledgments; Bibliography; Chapter 3. Recovery of relaxation rates in MRI T2-weighted brain images via exponential fitting; 3.1. Introduction; 3.2. The Prony method; 3.3. The separable nonlinear least squares approach; 3.4. Numerical results; 3.5. Conclusions and final remarks; 3.6. Appendix; 3.7. Acknowledgements; Bibliography; Chapter 4. Exponential time series in Lattice Quantum Field theory |
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4.1. Introduction4.2. Least-squares methods; 4.3. Bayesian methods; 4.4. Black-box methods; 4.5. Conclusion; Bibliography; Chapter 5. Solving separable nonlinear least squares problems with multiple datasets; 5.1. Introduction; 5.2. Applications; 5.3. The Jacobian; 5.4. Computational evidence; Bibliography; Chapter 6. Sum-of-exponentials models for time-resolved spectroscopy data; 6.1. Introduction; 6.2. Linear compartmental models; 6.3. Parameter estimation; 6.4. Implementation; 6.5. Standard error estimation; 6.6. Constraints on the parameters |
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6.7. Case study I: Time-resolved fluorescence emission measurements of photosystem I6.8. Case study II: Detection of protein-protein interactions; 6.9. Summary; Acknowledgments; Appendix; Bibliography; Chapter 7. Two exponential models for optically stimulated luminescence; 7.1. Introduction; 7.2. The OSL model; 7.3. The least squares solution and its sensitivity; 7.4. An alternative integral-equation approach; 7.5. The numerical methods; 7.6. Creating artificial data; 7.7. Simulation results; 7.8. Analysis of real data; 7.9. Conclusion; Bibliography |
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Chapter 8. Modelling type Ia supernova light curves8.1. Introduction; 8.2. The basic model; 8.3. Fitting the model to the B-passband observations; 8.4. Extending the model to U-, V-, R- and I-passband observations; 8.5. Conclusion; Acknowledgments; Disclaimer; Bibliography; Chapter 9. Accurate calculations of the high-frequency impedance matrix for VLSI interconnects and inductors above a multi-layer substrate: A VARPRO success story ; 9.1. Introduction; 9.2. Green's function computations; 9.3. Impedance computations; 9.4. Least square fits for multi-layer substrates |
| Summary |
Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision and Robotics. The most commonly used norm in the approximation by linear combinations of exponentials is the l2 norm (sum of squares of residuals), in which case one obtains a nonlinear separable least squares problem. A number of different methods have been proposed through the years to solve these types of problems and new applications appear daily. Necessary guidance is provided so that care should be taken when applying standard or simplified methods to it. The described methods take into account the separability between the linear and nonlinear parameters, which have been quite successful. The accessibility of good, publicly available software that has been very beneficial in many different fields is also considered. This Ebook covers the main solution methods (Variable Projections, Modified Prony) and also emphasizes the applications to different fields. It is considered essential reading for researchers and students in this field |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Exponential functions.
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MATHEMATICS -- Probability & Statistics -- Bayesian Analysis.
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Exponential functions
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| Form |
Electronic book
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| Author |
Pereyra, V. (Victor)
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Scherer, Godela
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| ISBN |
9781608050482 |
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1608050483 |
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