Steepest descent paths on simplicial meshes of arbitrary dimensions
This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Natali, Mattia [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013transfer abstract |
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| Schlagwörter: |
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| Umfang: |
10 |
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| Übergeordnetes Werk: |
Enthalten in: Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex - 2011, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:37 ; year:2013 ; number:6 ; pages:687-696 ; extent:10 |
| Links: |
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| DOI / URN: |
10.1016/j.cag.2013.05.003 |
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ELV032770383 |
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| 520 | |a This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. | ||
| 520 | |a This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. | ||
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10.1016/j.cag.2013.05.003 doi GBVA2013002000023.pica (DE-627)ELV032770383 (ELSEVIER)S0097-8493(13)00077-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 610 VZ 390 VZ 300 610 VZ 44.06 bkl Natali, Mattia verfasserin aut Steepest descent paths on simplicial meshes of arbitrary dimensions 2013transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. Gradient Elsevier Descendig arc Elsevier Multivariate function Elsevier Attene, Marco oth Ottonello, Giulio oth Enthalten in Elsevier Science Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex 2011 Amsterdam [u.a.] (DE-627)ELV015846202 volume:37 year:2013 number:6 pages:687-696 extent:10 https://doi.org/10.1016/j.cag.2013.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.06 Medizinsoziologie VZ AR 37 2013 6 687-696 10 045F 004 |
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10.1016/j.cag.2013.05.003 doi GBVA2013002000023.pica (DE-627)ELV032770383 (ELSEVIER)S0097-8493(13)00077-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 610 VZ 390 VZ 300 610 VZ 44.06 bkl Natali, Mattia verfasserin aut Steepest descent paths on simplicial meshes of arbitrary dimensions 2013transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. Gradient Elsevier Descendig arc Elsevier Multivariate function Elsevier Attene, Marco oth Ottonello, Giulio oth Enthalten in Elsevier Science Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex 2011 Amsterdam [u.a.] (DE-627)ELV015846202 volume:37 year:2013 number:6 pages:687-696 extent:10 https://doi.org/10.1016/j.cag.2013.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.06 Medizinsoziologie VZ AR 37 2013 6 687-696 10 045F 004 |
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10.1016/j.cag.2013.05.003 doi GBVA2013002000023.pica (DE-627)ELV032770383 (ELSEVIER)S0097-8493(13)00077-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 610 VZ 390 VZ 300 610 VZ 44.06 bkl Natali, Mattia verfasserin aut Steepest descent paths on simplicial meshes of arbitrary dimensions 2013transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. Gradient Elsevier Descendig arc Elsevier Multivariate function Elsevier Attene, Marco oth Ottonello, Giulio oth Enthalten in Elsevier Science Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex 2011 Amsterdam [u.a.] (DE-627)ELV015846202 volume:37 year:2013 number:6 pages:687-696 extent:10 https://doi.org/10.1016/j.cag.2013.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.06 Medizinsoziologie VZ AR 37 2013 6 687-696 10 045F 004 |
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10.1016/j.cag.2013.05.003 doi GBVA2013002000023.pica (DE-627)ELV032770383 (ELSEVIER)S0097-8493(13)00077-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 610 VZ 390 VZ 300 610 VZ 44.06 bkl Natali, Mattia verfasserin aut Steepest descent paths on simplicial meshes of arbitrary dimensions 2013transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. Gradient Elsevier Descendig arc Elsevier Multivariate function Elsevier Attene, Marco oth Ottonello, Giulio oth Enthalten in Elsevier Science Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex 2011 Amsterdam [u.a.] (DE-627)ELV015846202 volume:37 year:2013 number:6 pages:687-696 extent:10 https://doi.org/10.1016/j.cag.2013.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.06 Medizinsoziologie VZ AR 37 2013 6 687-696 10 045F 004 |
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10.1016/j.cag.2013.05.003 doi GBVA2013002000023.pica (DE-627)ELV032770383 (ELSEVIER)S0097-8493(13)00077-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 610 VZ 390 VZ 300 610 VZ 44.06 bkl Natali, Mattia verfasserin aut Steepest descent paths on simplicial meshes of arbitrary dimensions 2013transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. Gradient Elsevier Descendig arc Elsevier Multivariate function Elsevier Attene, Marco oth Ottonello, Giulio oth Enthalten in Elsevier Science Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex 2011 Amsterdam [u.a.] (DE-627)ELV015846202 volume:37 year:2013 number:6 pages:687-696 extent:10 https://doi.org/10.1016/j.cag.2013.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.06 Medizinsoziologie VZ AR 37 2013 6 687-696 10 045F 004 |
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Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex |
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Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex |
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Steepest descent paths on simplicial meshes of arbitrary dimensions |
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Steepest descent paths on simplicial meshes of arbitrary dimensions |
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Natali, Mattia |
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Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex |
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Phytochemical analysis, antioxidant and anti-inflammatory activities of Phyllanthus simplex |
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10.1016/j.cag.2013.05.003 |
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steepest descent paths on simplicial meshes of arbitrary dimensions |
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Steepest descent paths on simplicial meshes of arbitrary dimensions |
| abstract |
This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. |
| abstractGer |
This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. |
| abstract_unstemmed |
This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains. |
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Steepest descent paths on simplicial meshes of arbitrary dimensions |
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https://doi.org/10.1016/j.cag.2013.05.003 |
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Attene, Marco Ottonello, Giulio |
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