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L 31
Large scale inverse problems : : computational methods and applications in the earth sciences / / edited by Mike Cullen, Melina A. Freitag, Stefan Kindermann, Robert Scheichl. - Berlin ; ; Boston : : De Gruyter,, ©2013. - 1 online resource (ix, 203 pages) : : il. - (Radon Series on Computational and Applied Mathematics). - English. - Includes bibliographical references. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/C606FF6A-A3C6-4132-8102-D06DFFF2E942. - ISBN 9783110282269 (electronic bk.). - ISBN 3110282267 (electronic bk.). - ISBN 3110282224. - ISBN 9783110282221
Print version record.
Параллельные издания: Print version: : Scheichl, Robert. Large Scale Inverse Problems : Computational Methods and Applications in the Earth Sciences. - Berlin : De Gruyter, ©2013. - ISBN 9783110282221
Содержание:
Preface; Synergy of inverse problems and data assimilation techniques; 1 Introduction; 2 Regularization theory; 3 Cycling, Tikhonov regularization and 3DVar; 4 Error analysis; 5 Bayesian approach to inverse problems; 6 4DVar; 7 Kalman filter and Kalman smoother; 8 Ensemble methods; 9 Numerical examples; 9.1 Data assimilation for an advection-diffusion system; 9.2 Data assimilation for the Lorenz-95 system; 10 Concluding remarks; Variational data assimilation for very large environmental problems; 1 Introduction; 2 Theory of variational data assimilation.
2.1 Incremental variational data assimilation3 Practical implementation; 3.1 Model development; 3.2 Background error covariances; 3.3 Observation errors; 3.4 Optimization methods; 3.5 Reduced order approaches; 3.6 Issues for nested models; 3.7 Weak-constraint variational assimilation; 4 Summary and future perspectives; Ensemble filter techniques for intermittent data assimilation; 1 Bayesian statistics; 1.1 Preliminaries; 1.2 Bayesian inference; 1.3 Coupling of random variables; 1.4 Monte Carlo methods; 2 Stochastic processes; 2.1 Discrete time Markov processes.
2.2 Stochastic difference and differential equations2.3 Ensemble prediction and sampling methods; 3 Data assimilation and filtering; 3.1 Preliminaries; 3.2 SequentialMonte Carlo method; 3.3 Ensemble Kalman filter (EnKF); 3.4 Ensemble transform Kalman-Bucy filter; 3.5 Guided sequential Monte Carlo methods; 3.6 Continuous ensemble transform filter formulations; 4 Concluding remarks; Inverse problems in imaging; 1 Mathematicalmodels for images; 2 Examples of imaging devices; 2.1 Optical imaging; 2.2 Transmission tomography; 2.3 Emission tomography; 2.4 MR imaging; 2.5 Acoustic imaging.
2.6 Electromagnetic imaging3 Basic image reconstruction; 3.1 Deblurring and point spread functions; 3.2 Noise; 3.3 Reconstruction methods; 4 Missing data and prior information; 4.1 Prior information; 4.2 Undersampling and superresolution; 4.3 Inpainting; 4.4 Surface imaging; 5 Calibration problems; 5.1 Blind deconvolution; 5.2 Nonlinear MR imaging; 5.3 Attenuation correction in SPECT; 5.4 Blind spectral unmixing; 6 Model-based dynamic imaging; 6.1 Kinetic models; 6.2 Parameter identification; 6.3 Basis pursuit; 6.4 Motion and deformation models; 6.5 Advanced PDE models.
The lost honor of l2-based regularization1 Introduction; 2 l1-based regularization; 3 Poor data; 4 Large, highly ill-conditioned problems; 4.1 Inverse potential problem; 4.2 The effect of ill-conditioning on L1 regularization; 4.3 Nonlinear, highly ill-posed examples; 5 Summary; List of contributors.
~РУБ DDC 515.357
Рубрики: Inverse problems (Differential equations)
Applied mathematics.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Inverse problems (Differential equations)
Аннотация: This book is thesecond volume of three volume series recording the ""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking place in Linz, Austria, October 3-7, 2011. The volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications.
Доп.точки доступа:
Cullen, Michael J. P., \editor.\
Freitag, Melina A., (1980-) \editor.\
Kindermann, Stefan, (1972-) \editor.\
Scheichl, Robert, (1972-) \editor.\
L 31
Large scale inverse problems : : computational methods and applications in the earth sciences / / edited by Mike Cullen, Melina A. Freitag, Stefan Kindermann, Robert Scheichl. - Berlin ; ; Boston : : De Gruyter,, ©2013. - 1 online resource (ix, 203 pages) : : il. - (Radon Series on Computational and Applied Mathematics). - English. - Includes bibliographical references. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/C606FF6A-A3C6-4132-8102-D06DFFF2E942. - ISBN 9783110282269 (electronic bk.). - ISBN 3110282267 (electronic bk.). - ISBN 3110282224. - ISBN 9783110282221
Print version record.
Параллельные издания: Print version: : Scheichl, Robert. Large Scale Inverse Problems : Computational Methods and Applications in the Earth Sciences. - Berlin : De Gruyter, ©2013. - ISBN 9783110282221
Содержание:
Preface; Synergy of inverse problems and data assimilation techniques; 1 Introduction; 2 Regularization theory; 3 Cycling, Tikhonov regularization and 3DVar; 4 Error analysis; 5 Bayesian approach to inverse problems; 6 4DVar; 7 Kalman filter and Kalman smoother; 8 Ensemble methods; 9 Numerical examples; 9.1 Data assimilation for an advection-diffusion system; 9.2 Data assimilation for the Lorenz-95 system; 10 Concluding remarks; Variational data assimilation for very large environmental problems; 1 Introduction; 2 Theory of variational data assimilation.
2.1 Incremental variational data assimilation3 Practical implementation; 3.1 Model development; 3.2 Background error covariances; 3.3 Observation errors; 3.4 Optimization methods; 3.5 Reduced order approaches; 3.6 Issues for nested models; 3.7 Weak-constraint variational assimilation; 4 Summary and future perspectives; Ensemble filter techniques for intermittent data assimilation; 1 Bayesian statistics; 1.1 Preliminaries; 1.2 Bayesian inference; 1.3 Coupling of random variables; 1.4 Monte Carlo methods; 2 Stochastic processes; 2.1 Discrete time Markov processes.
2.2 Stochastic difference and differential equations2.3 Ensemble prediction and sampling methods; 3 Data assimilation and filtering; 3.1 Preliminaries; 3.2 SequentialMonte Carlo method; 3.3 Ensemble Kalman filter (EnKF); 3.4 Ensemble transform Kalman-Bucy filter; 3.5 Guided sequential Monte Carlo methods; 3.6 Continuous ensemble transform filter formulations; 4 Concluding remarks; Inverse problems in imaging; 1 Mathematicalmodels for images; 2 Examples of imaging devices; 2.1 Optical imaging; 2.2 Transmission tomography; 2.3 Emission tomography; 2.4 MR imaging; 2.5 Acoustic imaging.
2.6 Electromagnetic imaging3 Basic image reconstruction; 3.1 Deblurring and point spread functions; 3.2 Noise; 3.3 Reconstruction methods; 4 Missing data and prior information; 4.1 Prior information; 4.2 Undersampling and superresolution; 4.3 Inpainting; 4.4 Surface imaging; 5 Calibration problems; 5.1 Blind deconvolution; 5.2 Nonlinear MR imaging; 5.3 Attenuation correction in SPECT; 5.4 Blind spectral unmixing; 6 Model-based dynamic imaging; 6.1 Kinetic models; 6.2 Parameter identification; 6.3 Basis pursuit; 6.4 Motion and deformation models; 6.5 Advanced PDE models.
The lost honor of l2-based regularization1 Introduction; 2 l1-based regularization; 3 Poor data; 4 Large, highly ill-conditioned problems; 4.1 Inverse potential problem; 4.2 The effect of ill-conditioning on L1 regularization; 4.3 Nonlinear, highly ill-posed examples; 5 Summary; List of contributors.
Рубрики: Inverse problems (Differential equations)
Applied mathematics.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Inverse problems (Differential equations)
Аннотация: This book is thesecond volume of three volume series recording the ""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking place in Linz, Austria, October 3-7, 2011. The volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications.
Доп.точки доступа:
Cullen, Michael J. P., \editor.\
Freitag, Melina A., (1980-) \editor.\
Kindermann, Stefan, (1972-) \editor.\
Scheichl, Robert, (1972-) \editor.\
2.
Подробнее
B 92
Buffoni, Boris, (1965-).
Analytic Theory of Global Bifurcation. / Boris, Buffoni. - 1515/9781400884339. - [Б. м.] : Princeton University Press,, 2016. - 1 online resource ( час. мин.), 1515/9781400884339. - (Princeton Series in Applied Mathematics). - In English. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/7DD2689F-082C-486E-B2F6-C188564EA2F3. - ISBN 1400884330 (electronic bk.). - ISBN 9781400884339 (electronic bk.)
Print version record.
~РУБ DDC 515
Рубрики: Bifurcation theory.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Bifurcation theory.
Аннотация: Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory. Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis.
B 92
Buffoni, Boris, (1965-).
Analytic Theory of Global Bifurcation. / Boris, Buffoni. - 1515/9781400884339. - [Б. м.] : Princeton University Press,, 2016. - 1 online resource ( час. мин.), 1515/9781400884339. - (Princeton Series in Applied Mathematics). - In English. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/7DD2689F-082C-486E-B2F6-C188564EA2F3. - ISBN 1400884330 (electronic bk.). - ISBN 9781400884339 (electronic bk.)
Print version record.
Рубрики: Bifurcation theory.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Bifurcation theory.
Аннотация: Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory. Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis.
3.
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A 73
Arfaoui, Sabrine.
Wavelet Analysis on the Sphere. / Sabrine. Arfaoui. - Berlin/Boston, UNITED STATES : : De Gruyter,, 2017. - 1 online resource (156). - Includes bibliographical references. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/0139232F-C8DD-448E-8A43-5AAACFFD60D9. - ISBN 311048188X (electronic bk.). - ISBN 9783110481884 (electronic bk.). - ISBN 9783110481242 (electronic bk.). - ISBN 3110481243 (electronic bk.)
Print version record.
Параллельные издания: Print version: : Arfaoui, Sabrine. Wavelet Analysis on the Sphere : Spheroidal Wavelets. - Berlin/Boston : De Gruyter, ©2017. - ISBN 9783110481099
~РУБ DDC 515.2
Рубрики: Wavelets (Mathematics)
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Wavelets (Mathematics)
Аннотация: This monograph is concerned with wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials. ContentsReview of orthogonal polynomialsHomogenous polynomials and spherical harmonicsReview of special functionsSpheroidal-type wavelets Some applicationsSome applications.
A 73
Arfaoui, Sabrine.
Wavelet Analysis on the Sphere. / Sabrine. Arfaoui. - Berlin/Boston, UNITED STATES : : De Gruyter,, 2017. - 1 online resource (156). - Includes bibliographical references. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/0139232F-C8DD-448E-8A43-5AAACFFD60D9. - ISBN 311048188X (electronic bk.). - ISBN 9783110481884 (electronic bk.). - ISBN 9783110481242 (electronic bk.). - ISBN 3110481243 (electronic bk.)
Print version record.
Параллельные издания: Print version: : Arfaoui, Sabrine. Wavelet Analysis on the Sphere : Spheroidal Wavelets. - Berlin/Boston : De Gruyter, ©2017. - ISBN 9783110481099
Рубрики: Wavelets (Mathematics)
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Wavelets (Mathematics)
Аннотация: This monograph is concerned with wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials. ContentsReview of orthogonal polynomialsHomogenous polynomials and spherical harmonicsReview of special functionsSpheroidal-type wavelets Some applicationsSome applications.
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