On the Asymptotic Behavior of Scaled Singular Value and QR Decompositions
نویسندگان
چکیده
Asymptotic expressions are derived for the singular value decompositon of a matrix some of whose columns approach zero. Expressions are also derived for the QR factorization of a matrix some of whose rows approach zero. The expressions give insight into the method of weights for approximating the solutions of constrained least squares problems.
منابع مشابه
Some Asymptotic Behaviors Associated with Matrix Decompositions
We obtain several asymptotic results on the powers of a square matrix associated with SVD, QR decomposition and Cholesky decomposition.
متن کاملThe QR decomposition and the singular value decomposition in thesymmetrized max - plus algebra 1
In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...
متن کاملThe QR decomposition and the singular value decomposition in the symmetrized max-plus algebra∗
In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...
متن کاملOn Smooth Decompositions of Matrices
In this paper we consider smooth orthonormal decompositions of smooth time varying matrices. Among others, we consider QR–, Schur–, and singular value decompositions, and their block-analogues. Sufficient conditions for existence of such decompositions are given and differential equations for the factors are derived. Also generic smoothness of these factors is discussed.
متن کاملAsymptotic Behavior of Singular and Entropy Numbers for Some Riemann–liouville Type Operators
The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [15]) acting in weighted L spaces. In some cases singular value decompositions are obtained as well for these integral transforms. 2000 Mathematics Subject Classification: 47B06, 47B34, 47H50.
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:
دوره شماره
صفحات -
تاریخ انتشار 2010