Accurate ordering of eigenvectors and singular vectors without eigenvalues and singular values
نویسندگان
چکیده
منابع مشابه
On computing accurate singular values and eigenvalues . . .
[15] D. O'Leary and G. W. Stewart. Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices. [17] A. Sameh and D. Kuck. A parallel QR algorithm for symmetric tridiagonal matrices. [21] Zhonggang Zeng. The acyclic eigenproblem can be reduced to the arrowhead one. [22] Hongyuan Zha. A two-way chasing scheme for reducing a symmetric arrowhead matrix to tridiagonal form. Scientic ...
متن کاملAccurate computation of singular values and eigenvalues of symmetric matrices ∗
We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy.
متن کاملEigenvalues and Singular Values 10.1 Eigenvalue and Singular Value Decompositions
This chapter is about eigenvalues and singular values of matrices. Computational algorithms and sensitivity to perturbations are both discussed. An eigenvalue and eigenvector of a square matrix A are a scalar λ and a nonzero vector x so that Ax = λx. A singular value and pair of singular vectors of a square or rectangular matrix A are a nonnegative scalar σ and two nonzero vectors u and v so th...
متن کاملEigenvalues, singular values, and Littlewood-Richardson Coefficients
Chi-Kwong Li Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795, USA E-mail: [email protected] We briefly describe some recent results on inequalities relating the eigenvalues of the sum of Hermitian or real matrices, and how to use these them inequalities relating the eigenvalues and singular values of a matrix and its submatrices. These results are joint ...
متن کاملNotes on Eigenvalues, Singular Values and QR
for some nonzero vector x called an eigenvector. This is equivalent to writing (λI − A)x = 0 so, since x 6= 0, A− λI must be singular, and hence det(λI − A) = 0. From the (complicated!) definition of determinant, it follows that det(λI−A) is a polynomial in the variable λ with degree n, and this is called the characteristic polynomial. By the fundamental theorem of algebra (a nontrivial result)...
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: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00537-8