Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On the Jacobians of the Factors of the Truncated Singular Value Decomposition
View through CrossRef
HighlightsOn the Jacobians of the Factors of the Truncated Singular Value DecompositionThe aim of this paper is to derive analytical expressions for the Jacobians for the factors of the Truncated Singular Value Decomposition (TSVD) of a matrix. The starting point of this study is an earlier work by \cite{GratTshi16} on the second-order expansion of the truncated singular subspace decomposition. We consider the first-order Fréchet derivatives expressions found in that work to establish the Jacobians. We then specialize the found results to singular vectors and singular values. We show that our results are consistent with earlier works on particular cases. A numerical example is performed to confirm the validity of our theory.
Title: On the Jacobians of the Factors of the Truncated Singular Value Decomposition
Description:
HighlightsOn the Jacobians of the Factors of the Truncated Singular Value DecompositionThe aim of this paper is to derive analytical expressions for the Jacobians for the factors of the Truncated Singular Value Decomposition (TSVD) of a matrix.
The starting point of this study is an earlier work by \cite{GratTshi16} on the second-order expansion of the truncated singular subspace decomposition.
We consider the first-order Fréchet derivatives expressions found in that work to establish the Jacobians.
We then specialize the found results to singular vectors and singular values.
We show that our results are consistent with earlier works on particular cases.
A numerical example is performed to confirm the validity of our theory.
Related Results
Novedades sobre el enterramiento femenino de la Primera Edad del Hierro de Casa del Carpio (Belvís de la Jara, Toledo)
Novedades sobre el enterramiento femenino de la Primera Edad del Hierro de Casa del Carpio (Belvís de la Jara, Toledo)
Las características de la ubicación de la tumba de Casa del Carpio (Belvís de la Jara, Toledo), las circunstancias de su documentación, y lo excepcional del ajuar documentado han c...
APPLICATION OF SVD METHOD IN SOLVING INCORRECT GEODESIC PROBLEMS
APPLICATION OF SVD METHOD IN SOLVING INCORRECT GEODESIC PROBLEMS
The most reliable method for calculating linear equations of the least squares principle, which can be used to solve incorrect geodetic problems, is based on matrix factorization, ...
The Application of S‐transform Spectrum Decomposition Technique in Extraction of Weak Seismic Signals
The Application of S‐transform Spectrum Decomposition Technique in Extraction of Weak Seismic Signals
AbstractIn processing of deep seismic reflection data, when the frequency band difference between the weak useful signal and noise both from the deep subsurface is very small and h...
Projeto Terapêutico Singular: ferramenta de superação do GAP terapêutico em saúde mental
Projeto Terapêutico Singular: ferramenta de superação do GAP terapêutico em saúde mental
Objetivo: Relatar a experiência acadêmico-assistencial de estudantes de Enfermagem durante a construção conjunta de um projeto terapêutico singular com as equipes de atenção à saúd...
1D Self-Similar Fractals with Centro-Symmetric Jacobians: Asymptotics and Modular Data
1D Self-Similar Fractals with Centro-Symmetric Jacobians: Asymptotics and Modular Data
We establish the asymptotics of growing one-dimensional self-similar fractal graphs that are networks with multiple weighted edges between nodes. The asymptotics is described in te...
LITTER DECOMPOSITION IN Rhizophora sp. MANGROVE STANDS OF VARYING PLANTING AGES
LITTER DECOMPOSITION IN Rhizophora sp. MANGROVE STANDS OF VARYING PLANTING AGES
Information about litter decomposition in Rhizophora Sp. mangrove stands of different planting ages is very important to find out the main factors affecting the whole information o...
Nitrogen and Microelements Co-Drive the Decomposition of Typical Grass Litter in the Loess Plateau, China
Nitrogen and Microelements Co-Drive the Decomposition of Typical Grass Litter in the Loess Plateau, China
In grassland ecosystems, the decomposition of litter serves as a vital conduit for nutrient transfer between plants and soil. The aim of this study was to depict the dynamic proces...
Leaf litter diversity and structure of microbial decomposer communities modulate litter decomposition in aquatic systems
Leaf litter diversity and structure of microbial decomposer communities modulate litter decomposition in aquatic systems
AbstractLeaf litter decomposition is a major ecosystem process that can link aquatic to terrestrial ecosystems by flows of nutrients. Biodiversity and ecosystem functioning researc...