Smoothed Analysis of Moore-Penrose Inversion
نویسندگان
چکیده
We perform a smoothed analysis of the condition number of rectangular matrices. We prove that, asymptotically, the expected value of this condition number depends only of the elongation of the matrix, and not on the center and variance of the underlying probability distribution.
منابع مشابه
Penrose Inverse of Bidiagonal Matrices
Introduction. For a real m×n matrix A, the Moore–Penrose inverse A+ is the unique n×m matrix that satisfies the following four properties: AAA = A , AAA = A , (A+A)T = AA , (AA+)T = AA (see [1], for example). If A is a square nonsingular matrix, then A+ = A−1. Thus, the Moore–Penrose inversion generalizes ordinary matrix inversion. The idea of matrix generalized inverse was first introduced in ...
متن کاملAn Efficient Schulz-type Method to Compute the Moore-Penrose Inverse
A new Schulz-type method to compute the Moore-Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method converge with fourth-order. A wide set of numerical comparisons shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.
متن کاملThe reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...
متن کاملStructures preserved by generalized inversion and Schur complementation
In this paper we investigate the inheritance of certain structures under generalized matrix inversion. These structures contain the case of rank structures, and the case of displacement structures. We do this in an intertwined way, in the sense that we develop an argument that can be used for deriving the results for displacement structures from thoses for rank structures. We pay particular att...
متن کاملHermitian solutions to the system of operator equations T_iX=U_i.
In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...
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:
- SIAM J. Matrix Analysis Applications
دوره 31 شماره
صفحات -
تاریخ انتشار 2010