Handbook of Variational Methods for Nonlinear Geometric Data. 1st ed. 2020

種類:

電子ブック

責任表示:

edited by Philipp Grohs, Martin Holler, Andreas Weinmann

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Grohs, Philipp.
• Holler, Martin.
• Weinmann, Andreas.
• SpringerLink (Online service)

ISBN:

9783030313517 [3030313514]    

注記:

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 optimi
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 prov

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