Overcompleteness (original) (raw)
Overcompleteness is a concept from linear algebra that is widely used in mathematics, computer science, engineering, and statistics (usually in the form of overcomplete frames). It was introduced by R. J. Duffin and A. C. Schaeffer in 1952. In research areas such as signal processing and function approximation, overcompleteness can help researchers to achieve a more stable, more robust, or more compact decomposition than using a basis.
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| dbo:abstract | Overcompleteness is a concept from linear algebra that is widely used in mathematics, computer science, engineering, and statistics (usually in the form of overcomplete frames). It was introduced by R. J. Duffin and A. C. Schaeffer in 1952. Formally, a subset of the vectors of a Banach space , sometimes called a "system", is complete if every element in can be approximated arbitrarily well in norm by finite linear combinations of elements in . A complete system is additionally overcomplete if there exists a which can be removed from the system while maintaining completeness (i.e., ). In this sense, the system contains more vectors than necessary to be complete, hence "overcomplete". In research areas such as signal processing and function approximation, overcompleteness can help researchers to achieve a more stable, more robust, or more compact decomposition than using a basis. (en) |
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| rdfs:comment | Overcompleteness is a concept from linear algebra that is widely used in mathematics, computer science, engineering, and statistics (usually in the form of overcomplete frames). It was introduced by R. J. Duffin and A. C. Schaeffer in 1952. In research areas such as signal processing and function approximation, overcompleteness can help researchers to achieve a more stable, more robust, or more compact decomposition than using a basis. (en) |
| rdfs:label | Overcompleteness (en) |
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