Overcompleteness
Concept in linear algebra / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Overcompleteness?
Summarize this article for a 10 year old
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.[1]
This article may be too technical for most readers to understand. (October 2021) |
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 .[2] A system is called overcomplete if it contains more vectors than necessary to be complete, i.e., there exist that can be removed from the system such that remains complete. 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.[3]