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overcompre
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There are 10 letters in OVERCOMPRE ( C3E1M3O1P3R1V4 )
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| Overcompre might refer to |
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In linear algebra, a subset of the vectors * * * * { * * ϕ * * i * * * * } * * i * ∈ * J * * * * * {\displaystyle \{\phi _{i}\}_{i\in J}} * of a Banach space * * * * X * * * {\displaystyle X} * , sometimes called a "system", is complete if every element in * * * * X * * * {\displaystyle X} * can be approximated arbitrarily well in norm by finite linear combinations of elements in * * * * { * * ϕ * * i * * * * } * * i * ∈ * J * * * * * {\displaystyle \{\phi _{i}\}_{i\in J}} * . Such a complete system is overcomplete if removal of a * * * * * ϕ * * j * * * * * {\displaystyle \phi _{j}} * from the system results in a system (i.e., * * * * { * * ϕ * * i * * * * } * * i * ∈ * J * ∖ * { * j * } * * * * * {\displaystyle \{\phi _{i}\}_{i\in J\backslash \{j\}}} * ) that is still complete. In different research, 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. Overcomplete frames are widely used in mathematics, computer science, engineering, and statistics. |