dc.creator | Akritas, A. G. | en |
dc.creator | Malaschonok, G. I. | en |
dc.date.accessioned | 2015-11-23T10:21:53Z | |
dc.date.available | 2015-11-23T10:21:53Z | |
dc.date.issued | 2004 | |
dc.identifier | 10.1016/j.matcom.2004.05.005 | |
dc.identifier.issn | 0378-4754 | |
dc.identifier.uri | http://hdl.handle.net/11615/25412 | |
dc.description.abstract | Let A be an m x n matrix with m greater than or equal to n. Then one form of the singular-value decomposition of A is A = U-T SigmaV, where U and V are orthogonal and Sigma is square diagonal. That is, UUT = I-rank(A), VVT = I-rank(A), U is rank(A) x m, V is rank(A) x n and [GRAPHICS] is a rank (A) x rank(A) diagonal matrix. In addition sigma(1) greater than or equal to sigma(2) greater than or equal to... greater than or equal to sigma(rank)(A) > 0. The sigma(i)'s are called the singular values of A and their number is equal to the rank of A. The ratio sigma(1) /sigma(rank)(A) can be regarded as a condition number of the matrix A. It is easily verified that the singular-value decomposition can be also written as [GRAPHICS] The matrix u(i)(T) v(i) is the outerproduct of the i-th row of U with the corresponding row of V. Note that each of these matrices can be stored using only m + n locations rather than mn locations. | en |
dc.source | Mathematics and Computers in Simulation | en |
dc.source.uri | <Go to ISI>://WOS:000224205900003 | |
dc.subject | applications | en |
dc.subject | singular-value decompositions | en |
dc.subject | hanger | en |
dc.subject | stretcher | en |
dc.subject | aligner | en |
dc.subject | Computer Science, Interdisciplinary Applications | en |
dc.subject | Computer Science, | en |
dc.subject | Software Engineering | en |
dc.subject | Mathematics, Applied | en |
dc.title | Applications of singular-value decomposition (SVD) | en |
dc.type | journalArticle | en |