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7 Manifold interpolation (Q3384277)

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Language	Label	Description	Also known as
English	7 Manifold interpolation	scientific article

Statements

scholarly article

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7 Manifold interpolation (English)

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Ralf Zimmermann

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System- and Data-Driven Methods and Algorithms

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publication date

15 December 2021

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zbMATH Keywords

parametric model reduction

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matrix manifold

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interpolation

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Riemannian computing

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Riemannian normal coordinates

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1515/9783110498967-007

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Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds

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Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

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On the Convergence of Gradient Descent for Finding the Riemannian Center of Mass

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Choosing roots of polynomials smoothly

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Lie Groups and Geometric Aspects of Isometric Actions

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An Online Method for Interpolating Linear Parametric Reduced-Order Models

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The left invariant metric in the general linear group

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Geometric Means in a Novel Vector Space Structure on Symmetric Positive‐Definite Matrices

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Missing Point Estimation in Models Described by Proper Orthogonal Decomposition

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An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations

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Geometric mean and geodesic regression on Grassmannians

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A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

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Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank

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Endpoint Geodesics on the Stiefel Manifold Embedded in Euclidean Space

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Radial Basis Functions

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On the geometry of Riemannian cubic polynomials.

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A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems

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Statistics on the Stiefel manifold: theory and applications

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Nonlinear Model Reduction via Discrete Empirical Interpolation

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Positive Definite Matrices: Data Representation and Applications to Computer Vision

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The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces

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Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis

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The Geometry of Algorithms with Orthogonality Constraints

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Interpolation-based reduced-order modelling for steady transonic flows via manifold learning

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Geometric Methods and Applications

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Introduction to the theory of Lie groups. Translated from the French by Urmie Ray

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Quasi-interpolation in Riemannian manifolds

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Efficient reduced models and<i>a posteriori</i>error estimation for parametrized dynamical systems by offline/online decomposition

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Lie Groups, Lie Algebras, and Representations

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Reduced-order models for parameter dependent geometries based on shape sensitivity analysis

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Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

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Functions of Matrices

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Rolling Stiefel manifolds

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A reduced-order method for simulation and control of fluid flows

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A two-step algorithm of smooth spline generation on Riemannian manifolds

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Kernels on Riemannian Manifolds

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Riemannian center of mass and mollifier smoothing

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Canonical Correlation Analysis on SPD(n) Manifolds

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Quotient Geometry with Simple Geodesics for the Manifold of Fixed-Rank Positive-Semidefinite Matrices

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Algorithmic advances in Riemannian geometry and applications. For machine learning, computer vision, statistics, and optimization

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From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings

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A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices

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The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data

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Continuous Mode Interpolation for Control-Oriented Models of Fluid Flow

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De Casteljau's algorithm on manifolds

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A real time procedure for affinely dependent parametric model order reduction using interpolation on Grassmann manifolds

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Cubic Splines on Curved Spaces

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Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements

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A Riemannian framework for tensor computing

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Bézier curves and \(C^{2}\) interpolation in Riemannian manifolds

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Multiscale Representations for Manifold-Valued Data

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Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations

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A gradient-descent method for curve fitting on Riemannian manifolds

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\(C^1\) interpolating Bézier path on Riemannian manifolds, with applications to 3D shape space

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Geodesic finite elements of higher order

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Galerkin Models Enhancements for Flow Control

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A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank

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DIFFERENTIAL GEOMETRY OF GRASSMANN MANIFOLDS

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Gradient-enhanced surrogate modeling based on proper orthogonal decomposition

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A Locally Parametrized Reduced-Order Model for the Linear Frequency Domain Approach to Time-Accurate Computational Fluid Dynamics

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Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information

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A Matrix-Algebraic Algorithm for the Riemannian Logarithm on the Stiefel Manifold under the Canonical Metric

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Hermite Interpolation and Data Processing Errors on Riemannian Matrix Manifolds

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Parametric model reduction via interpolating orthonormal bases

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An Accelerated Greedy Missing Point Estimation Procedure

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Identifiers

zbMATH Open document ID

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10.1515/9783110498967-007

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3384277

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