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词汇 Overcompleteness
分类 英语词汇 英语翻译词典
释义

Overcompleteness

英语百科

Overcompleteness

A subset \{\phi_i\}_{i\in J} of a Banach space X, sometimes called a "system", is complete if every element in X can be approximated arbitrarily well in norm by finite linear combinations of elements in \{\phi_i\}_{i\in J}. Such a complete system is overcomplete if removal of a \phi_j from the system results in a system (i.e., \{\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.

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