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Published in:
2016 | OriginalPaper | Chapter
On the Algebraic and Geometric Structure of RB Methods
Authors : Alfio Quarteroni, Andrea Manzoni, Federico Negri
Published in: Reduced Basis Methods for Partial Differential Equations
Publisher: Springer International Publishing
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RB methods are revisited from both an algebraic and a geometric standpoint. A number of relationships between the Galerkin RB approximation (as well as least-squares RB approximation) and the Galerkin high-fidelity approximation (3.11) are highlighted, for the purpose of illustrating, in a more fitting way and from a different perspective, the mathematical structure underpinning RB methods. The key role played by the transformation matrix in defining orthogonal and oblique projections is emphasized.