منابع مشابه
Matrix Completion Problems
Matrix completion problems are concerned with determining whether partially speciied matrices can be completed to fully speciied matrices satisfying certain prescribed properties. In this article we survey some results and provide references about these problems for the following matrix properties: positive semideenite matrices, Euclidean distance matrices, completely positive matrices, contrac...
متن کاملEuclidean distance matrix completion problems
A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partially-specified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries to make A a Euclidean distance matrix. We survey three different approaches to solving the EDMCP.We advoca...
متن کاملOn perturbations of matrix pencils with real spectra. II
A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and à be two n×n Hermitian matrices, and let λ1, . . . , λn and λ̃1, . . . , λ̃n be their eigenvalues arranged in ascending order. Then ∣∣∣∣∣∣diag (λ1 − λ̃1, . . . , λn − λ̃n)∣∣∣∣∣∣ ≤ ∣∣∣∣∣∣A− Ã∣∣∣∣∣∣ for any unitarily invariant norm ||| · |||. In this paper, we generalize this to the perturbation ...
متن کاملBalancing Regular Matrix Pencils
In this paper we present a new diagonal balancing technique for regular matrix pencils λB − A, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired from the balancing technique of a square matrix A and has a comparable complexity. Upon convergence, the diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also s...
متن کاملStratification of Matrix Pencils
To design a modern control system is a complex problem which requires high qualitative software. This software must be based on robust algorithms and numerical stable methods which both can provide quantitative as well as qualitative information. In this Licentiate Thesis, the focus is on the qualitative information. The aim is to grasp the underlying advanced mathematical theory and provide al...
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: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.03.021