A Least Squares Decomposition Theorem with Applications to Data Compaction.
Abstract
The subject of this dissertation is a family of algorithms which can be used as a method of data compaction. The algorithms are developed and their properties discussed with regard to matrix compaction. The basis of the algorithms is a least squares decomposition theorem which supplies analytic expressions for obtaining approximations to the matrix entries. In developing the decomposition theorem, a sub-ring of matrices, bimatrices, is used and their properties are described. A Moore-Penrose generalized inverse developed as a function of bimatrices is used in the solution of the least squares problem. This dissertation also contains discussions of the error matrices produced by the algorithms, the compaction ratios of the algorithms and the convergence properties of the algorithms. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0715000
Entities
People
- Bernard A. Glassman
Organizations
- University of California, Los Angeles