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Grohs, Philipp.

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Handbook of variational methods for nonlinear geometric data

Record Type:	Electronic resources : Monograph/item
Title/Author:	Handbook of variational methods for nonlinear geometric data/ edited by Philipp Grohs, Martin Holler, Andreas Weinmann.
other author:	Grohs, Philipp.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xxvi, 701 p. :ill., digital ;24 cm.
[NT 15003449]:	1. Geometric Finite Elements -- 2. Non-smooth variational regularization for processing manifold-valued data -- 3. Lifting methods for manifold-valued variational problems -- 4. Geometric subdivision and multiscale transforms -- 5. Variational Methods for Discrete Geometric Functionals -- 6 Variational methods for fluid-structure interactions -- 7. Convex lifting-type methods for curvature regularization -- 8. Assignment Flows -- 9. Geometric methods on low-rank matrix and tensor manifolds -- 10. Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces -- 11. Advances in Geometric Statistics for manifold dimension reduction -- 12. Deep Variational Inference.- 13. Shape Analysis of Functional Data -- 14. Statistical Analysis of Trajectories of Multi-Modality Data -- 15. Geometric Metrics for Topological Representations -- 16. On Geometric Invariants, Learning, and Recognition of Shapes and Forms -- 17. Sub-Riemannian Methods in Shape Analysis -- 18. First order methods for optimization on Riemannian manifolds -- 19. Recent Advances in Stochastic Riemannian Optimization -- 20. Averaging symmetric positive-definite matrices -- 21. Rolling Maps and Nonlinear Data -- 22. Manifold-valued Data in Medical Imaging Applications -- 23. The Riemannian and Affine Geometry of Facial Expression and Action Recognition -- 24. Biomedical Applications of Geometric Functional Data Analysis.
Contained By:	Springer eBooks
Subject:	Calculus of variations - Handbooks, manuals, etc. -
Online resource:	https://doi.org/10.1007/978-3-030-31351-7
ISBN:	9783030313517

Handbook of variational methods for nonlinear geometric data
Handbook of variational methods for nonlinear geometric data[electronic resource] /edited by Philipp Grohs, Martin Holler, Andreas Weinmann. - Cham :Springer International Publishing :2020. - xxvi, 701 p. :ill., digital ;24 cm.

1. Geometric Finite Elements -- 2. Non-smooth variational regularization for processing manifold-valued data -- 3. Lifting methods for manifold-valued variational problems -- 4. Geometric subdivision and multiscale transforms -- 5. Variational Methods for Discrete Geometric Functionals -- 6 Variational methods for fluid-structure interactions -- 7. Convex lifting-type methods for curvature regularization -- 8. Assignment Flows -- 9. Geometric methods on low-rank matrix and tensor manifolds -- 10. Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces -- 11. Advances in Geometric Statistics for manifold dimension reduction -- 12. Deep Variational Inference.- 13. Shape Analysis of Functional Data -- 14. Statistical Analysis of Trajectories of Multi-Modality Data -- 15. Geometric Metrics for Topological Representations -- 16. On Geometric Invariants, Learning, and Recognition of Shapes and Forms -- 17. Sub-Riemannian Methods in Shape Analysis -- 18. First order methods for optimization on Riemannian manifolds -- 19. Recent Advances in Stochastic Riemannian Optimization -- 20. Averaging symmetric positive-definite matrices -- 21. Rolling Maps and Nonlinear Data -- 22. Manifold-valued Data in Medical Imaging Applications -- 23. The Riemannian and Affine Geometry of Facial Expression and Action Recognition -- 24. Biomedical Applications of Geometric Functional Data Analysis.

This book explains how variational methods have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

ISBN: 9783030313517

Standard No.: 10.1007/978-3-030-31351-7doiSubjects--Topical Terms:

3450328
Calculus of variations
--Handbooks, manuals, etc.

LC Class. No.: QA315 / .H363 2020

Dewey Class. No.: 515.64

Handbook of variational methods for nonlinear geometric data
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245 0 0 $a Handbook of variational methods for nonlinear geometric data $h [electronic resource] / $c edited by Philipp Grohs, Martin Holler, Andreas Weinmann.
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505 0 $a 1. Geometric Finite Elements -- 2. Non-smooth variational regularization for processing manifold-valued data -- 3. Lifting methods for manifold-valued variational problems -- 4. Geometric subdivision and multiscale transforms -- 5. Variational Methods for Discrete Geometric Functionals -- 6 Variational methods for fluid-structure interactions -- 7. Convex lifting-type methods for curvature regularization -- 8. Assignment Flows -- 9. Geometric methods on low-rank matrix and tensor manifolds -- 10. Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces -- 11. Advances in Geometric Statistics for manifold dimension reduction -- 12. Deep Variational Inference.- 13. Shape Analysis of Functional Data -- 14. Statistical Analysis of Trajectories of Multi-Modality Data -- 15. Geometric Metrics for Topological Representations -- 16. On Geometric Invariants, Learning, and Recognition of Shapes and Forms -- 17. Sub-Riemannian Methods in Shape Analysis -- 18. First order methods for optimization on Riemannian manifolds -- 19. Recent Advances in Stochastic Riemannian Optimization -- 20. Averaging symmetric positive-definite matrices -- 21. Rolling Maps and Nonlinear Data -- 22. Manifold-valued Data in Medical Imaging Applications -- 23. The Riemannian and Affine Geometry of Facial Expression and Action Recognition -- 24. Biomedical Applications of Geometric Functional Data Analysis.
520 $a This book explains how variational methods have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.
650 0 $a Calculus of variations $v Handbooks, manuals, etc. $3 3450328
650 0 $a Geometry $v Handbooks, manuals, etc. $3 3450329
650 1 4 $a Computational Mathematics and Numerical Analysis. $3 891040
650 2 4 $a Math Applications in Computer Science. $3 891004
650 2 4 $a Image Processing and Computer Vision. $3 891070
650 2 4 $a Mathematical Applications in Computer Science. $3 1567978
700 1 $a Grohs, Philipp. $3 3450325
700 1 $a Holler, Martin. $3 3450326
700 1 $a Weinmann, Andreas. $3 3450327
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