On condition numbers for Moore-Penrose inverse and linear least squares problem involving Kronecker products
نویسندگان
چکیده
1School of Mathematics and Statistics, Key Laboratory for Applied Statistics of MOE, Northeast Normal University, Chang Chun 130024, China 2School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China 3School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China 4Department of Computing and Software, McMaster University, Hamilton, Ontario L8S 4K1, Canada
منابع مشابه
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and, in particular, a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this paper, we give explicit expressi...
متن کاملOn level-2 condition number for the weighted Moore-Penrose inverse
In this paper, we present characterizations for the level-2 condition number of the weighted Moore–Penrose inverse, i.e., condMN (A) ≤ cond [2] MN (A) ≤ condMN (A)+ 1, where condMN (A) is the condition number of the weighted Moore–Penrose inverse of a rectangular matrix and cond [2] MN (A) is the level-2 condition number of this problem. This paper extends the result by Cucker, Diao and Wei [F....
متن کاملOn the Solution of Constrained and Weighted Linear Least Squares Problems
Important problems in many scientific computational areas are least squares problems. The problem of constraint least squares with full column weight matrix is a class of these problems. In this presentation, we are concerned with the connection between the condition numbers and the rounding error in the solution of the problem of constrained and weighted linear least squares. The fact that thi...
متن کاملA generalization of the Moore-Penrose inverse related to matrix subspaces of Cn×m
A natural generalization of the classical Moore-Penrose inverse is presented. The so-called S-Moore-Penrose inverse of a m × n complex matrix A, denoted by AS, is defined for any linear subspace S of the matrix vector space Cn×m. The S-Moore-Penrose inverse AS is characterized using either the singular value decomposition or (for the nonsingular square case) the orthogonal complements with resp...
متن کاملMonotonicity and Iterative Approximations Involving Rectangular Matrices
A new characterization of row-monotone matrices is given and is related to the Moore-Penrose generalized inverse. The M-matrix concept is extended to rectangular matrices with full column rank. A structure theorem is provided for all matrices A with full column rank for which the generalized inverse A+ & 0. These results are then used to investigate convergent splittings of rectangular matrices...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Numerical Lin. Alg. with Applic.
دوره 20 شماره
صفحات -
تاریخ انتشار 2013