M. On a theorem by Eckart and Young . Psychometrika , 1963 , 28 , 259 – 263 .Johnson RM ( 1963 ) On the theorem stated by Eckart and Young . Psychometrika 28 , 259 – 263 .Johnson, R. M. (1963). On a theorem stated by Eckart and Young, Psychometrika, 28, 259–263. Math...
The Eckart-Young Theorem. Suppose a matrix A∈Rm×n has an SVD-decomposition A=UΣVT . Let k<r=rank(A) and truncated matrix Ak=∑i=1kσiuiviT, then, for any matrix B of rank k , the minimal error is achieved with Ak : minrank(B)=k||A−B||2=||A−Ak||2=σk+1. Th...
We present a simple proof of the following theorem of Wiegmann, but in principle given earlier by Eckart and Young: THEOREM If {Ai) is a set of complex r – s matrices such thatA A andA A are Hermitian for all i andj, then there exist unitary matrices P and Q such that for each...
We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.关键词: Eckart and Young theorem moreau envelopes rank minimization problems DOI: 10.1051/ro/2013040 被引量: 3 ...
Golub G, Hoffman A, Stewart G (1987) A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Linear Algebra Appl 88:317–327 MathSciNetG. H. Golub, A. Hoffman, and G. W. Stewart. A generalization of the Eckart-Young matrix approximation theorem. Linear Algebra and Its ...
1. Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problem [J] . Wei MS. Linear Algebra and its Applications . 1998,第2a3期 机译:Eckart-Young-Mirsky定理的摄动理论和受约束的总最小二乘问题 2. PERTURBATION THEORY FOR ORTHOGONAL PROJECTION METHOD...
theoryfortheEckart-Young- Mirskytheoremandtheconstrained total leastsquaresproblem ’ MushengWei DepartmentofMathematics,EastChinaNormalUniversity,Shanghai200062, People’sRepublicofChina Received 2July1991;receivedinrevisedform4February1998;accepted12February1998 ...
AGeneralization of theEckart-Young-Mirsky MatrixApproximation Theorem G.H.Golub* DepartmentofComputerScience StanfordUniversity Stanford,California94305 AlanHoffman MathematicsScienceDepartment ThomasJ.WatsonResearchCenter G.W.Stewart’ DepartmentofComputerScience andInstituteforPhysicalScienceandTechnology Universityof...
We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.关键词: Eckart and Young theorem moreau envelopes rank min-imization problems DOI: 10.1051/ro/2013040 被引量: 3 ...
Generalized Eckart-Young theoremLocally reduced-rank optimal filtersSingular value decomposition (SVD)The Generalized Eckart- Young problem is a problem of finding a matrix minimizing a real valued quadratic matrix function over the set of all matrices of which rank does not exceed a pre-specified ...