FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2786954031> ?p ?o ?g. }

• W2786954031 abstract "A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the limit of large data. Simultaneously, the spectral approach decouples the memory requirements from the amount of data points and ambient space dimension. To achieve this, the exterior calculus is reformulated entirely in terms of the eigenvalues and eigenfunctions of the Laplacian operator on functions. The exterior derivatives of these eigenfunctions (and their wedge products) are shown to form a frame (a type of spanning set) for appropriate $L^2$ spaces of $k$-forms, as well as higher-order Sobolev spaces. Formulas are derived to express the Laplace-de Rham operators on forms in terms of the eigenfunctions and eigenvalues of the Laplacian on functions. By representing the Laplace-de Rham operators in this frame, spectral convergence results are obtained via Galerkin approximation techniques. Numerical examples demonstrate accurate recovery of eigenvalues and eigenforms of the Laplace-de Rham operator on 1-forms. The correct Betti numbers are obtained from the kernel of this operator approximated from data sampled on several orientable and non-orientable manifolds, and the eigenforms are visualized via their corresponding vector fields. These vector fields form a natural orthonormal basis for the space of square-integrable vector fields, and are ordered by a Dirichlet energy functional which measures oscillatory behavior. The spectral framework also shows promising results on a non-smooth example (the Lorenz 63 attractor), suggesting that a spectral formulation of exterior calculus may be feasible in spaces with no differentiable structure." @default.
• W2786954031 created "2018-02-23" @default.
• W2786954031 creator A5022515123 @default.
• W2786954031 creator A5076538541 @default.
• W2786954031 date "2018-02-04" @default.
• W2786954031 modified "2023-09-22" @default.
• W2786954031 title "Spectral exterior calculus." @default.
• W2786954031 cites W1522382323 @default.
• W2786954031 cites W1594387031 @default.
• W2786954031 cites W1674244219 @default.
• W2786954031 cites W1853432610 @default.
• W2786954031 cites W1976058996 @default.
• W2786954031 cites W1984032850 @default.
• W2786954031 cites W2007115787 @default.
• W2786954031 cites W2019398782 @default.
• W2786954031 cites W2034833521 @default.
• W2786954031 cites W2035556143 @default.
• W2786954031 cites W2039361027 @default.
• W2786954031 cites W2045688818 @default.
• W2786954031 cites W2048026906 @default.
• W2786954031 cites W2050507755 @default.
• W2786954031 cites W2057935334 @default.
• W2786954031 cites W2077180490 @default.
• W2786954031 cites W2092284067 @default.
• W2786954031 cites W2094204876 @default.
• W2786954031 cites W2097308346 @default.
• W2786954031 cites W2103829273 @default.
• W2786954031 cites W2115755118 @default.
• W2786954031 cites W2120103450 @default.
• W2786954031 cites W2138486270 @default.
• W2786954031 cites W2141394518 @default.
• W2786954031 cites W2163581538 @default.
• W2786954031 cites W2167469018 @default.
• W2786954031 cites W2225711375 @default.
• W2786954031 cites W2230899220 @default.
• W2786954031 cites W2703993429 @default.
• W2786954031 cites W2962936676 @default.
• W2786954031 cites W2962963464 @default.
• W2786954031 cites W2963013180 @default.
• W2786954031 cites W2963111412 @default.
• W2786954031 cites W2963186138 @default.
• W2786954031 cites W2963355980 @default.
• W2786954031 cites W2963425138 @default.
• W2786954031 cites W2963626317 @default.
• W2786954031 cites W2963687408 @default.
• W2786954031 cites W2963954124 @default.
• W2786954031 cites W2964084755 @default.
• W2786954031 cites W2976645955 @default.
• W2786954031 cites W3101974274 @default.
• W2786954031 cites W3103476862 @default.
• W2786954031 cites W423603040 @default.
• W2786954031 cites W4882049 @default.
• W2786954031 hasPublicationYear "2018" @default.
• W2786954031 type Work @default.
• W2786954031 sameAs 2786954031 @default.
• W2786954031 citedByCount "2" @default.
• W2786954031 countsByYear W27869540312019 @default.
• W2786954031 countsByYear W27869540312020 @default.
• W2786954031 crossrefType "posted-content" @default.
• W2786954031 hasAuthorship W2786954031A5022515123 @default.
• W2786954031 hasAuthorship W2786954031A5076538541 @default.
• W2786954031 hasConcept C104317684 @default.
• W2786954031 hasConcept C121332964 @default.
• W2786954031 hasConcept C128803854 @default.
• W2786954031 hasConcept C134306372 @default.
• W2786954031 hasConcept C154249771 @default.
• W2786954031 hasConcept C158448853 @default.
• W2786954031 hasConcept C158693339 @default.
• W2786954031 hasConcept C165700671 @default.
• W2786954031 hasConcept C17020691 @default.
• W2786954031 hasConcept C185592680 @default.
• W2786954031 hasConcept C202444582 @default.
• W2786954031 hasConcept C33923547 @default.
• W2786954031 hasConcept C55493867 @default.
• W2786954031 hasConcept C5806529 @default.
• W2786954031 hasConcept C62520636 @default.
• W2786954031 hasConcept C86339819 @default.
• W2786954031 hasConcept C99730327 @default.
• W2786954031 hasConceptScore W2786954031C104317684 @default.
• W2786954031 hasConceptScore W2786954031C121332964 @default.
• W2786954031 hasConceptScore W2786954031C128803854 @default.
• W2786954031 hasConceptScore W2786954031C134306372 @default.
• W2786954031 hasConceptScore W2786954031C154249771 @default.
• W2786954031 hasConceptScore W2786954031C158448853 @default.
• W2786954031 hasConceptScore W2786954031C158693339 @default.
• W2786954031 hasConceptScore W2786954031C165700671 @default.
• W2786954031 hasConceptScore W2786954031C17020691 @default.
• W2786954031 hasConceptScore W2786954031C185592680 @default.
• W2786954031 hasConceptScore W2786954031C202444582 @default.
• W2786954031 hasConceptScore W2786954031C33923547 @default.
• W2786954031 hasConceptScore W2786954031C55493867 @default.
• W2786954031 hasConceptScore W2786954031C5806529 @default.
• W2786954031 hasConceptScore W2786954031C62520636 @default.
• W2786954031 hasConceptScore W2786954031C86339819 @default.
• W2786954031 hasConceptScore W2786954031C99730327 @default.
• W2786954031 hasLocation W27869540311 @default.
• W2786954031 hasOpenAccess W2786954031 @default.
• W2786954031 hasPrimaryLocation W27869540311 @default.
• W2786954031 hasRelatedWork W1993483385 @default.
• W2786954031 hasRelatedWork W2026721917 @default.

• next