Multiplicative perturbation bounds for weighted unitary polar factor
نویسندگان
چکیده
منابع مشابه
Multiplicative Perturbation Bounds for Weighted Unitary Polar Factor
The multiplicative perturbation bounds for weighted unitary polar factor are considered in the weighted unitary invariant norm, weighted spectral norm, and weighted Frobenius norm in this paper. As the special cases, new bounds for subunitary and unitary polar factor are also derived. These new bounds improve the corresponding results published recently to some extent. Mathematics subject class...
متن کاملNew Perturbation Bounds for the Unitary Polar Factor
Let A be an m n (m n) complex matrix. It is known that there is a unique polar decomposition A = QH, where Q Q = I, the n n identity matrix, and H is positive de nite, provided A has full column rank. This note addresses the following question: how much may Q change if A is perturbed? For the square case m = n our bound, which is valid for any unitarily invariant norm, is sharper and simpler th...
متن کاملRelative and Absolute Perturbation Bounds for Weighted Polar Decomposition
Let Cm×n, Cm×n r , C m ≥ , C m > , and In denote the set of m × n complex matrices, subset of Cm×n consisting of matrices with rank r, set of the Hermitian nonnegative definite matrices of order m, subset of C ≥ consisting of positive-definite matrices and n × n unit matrix, respectively. Without specification, we always assume that m > n >max{r, s} and the given weight matrices M ∈ C > ,N ∈ C ...
متن کاملPerturbation Bounds for the Polar Decomposition
Let M n (F) denote the space of matrices over the eld F. Given A2 M n (F) deene jAj (A A) 1=2 and U(A) AjAj ?1 assuming A is nonsingular. Let 1 (A) 2 (A) n (A) 0 denote the ordered singular values of A. We obtain majorization results relating the singular values of U(A + A) ? U(A) and those of A and A. In particular we show that if A; A2 M n (R) and 1 ((A) < n (A) then for any unitarily invaria...
متن کاملNew Perturbation Bounds for Nonnegative and Positive Polar Factors
The changes in the nonnegative and positive polar factors of generalized polar decomposition and polar decomposition are studied under the additive perturbation. Some new perturbation bounds are obtained. These bounds are different from precious ones in form and measure and, in some cases, may be smaller than the corresponding existing ones. Furthermore, the corresponding perturbation bounds fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2010
ISSN: 1331-4343
DOI: 10.7153/mia-13-37