نتایج جستجو برای: girectional majorization

تعداد نتایج: 1034  

Journal: :bulletin of the iranian mathematical society 2011
a. armandnejad h. heydari

2010
Hossein Heydari Jong Kim

Let F and Fm be the usual spaces of n-dimensional column and m-dimensional row vectors on F, respectively, where F is the field of real or complex numbers. In this paper, the relations gsmajorization, lgw-majorization, and rgw-majorization are considered on F and Fm. Then linear maps T : F → F preserving lgw-majorization or gs-majorization and linear maps S : Fn → Fm, preserving rgw-majorizatio...

1997
Geir Dahl

There are important connections between majorization and convex polyhedra. Both weak majorization and majorization are preorders related to certain simple convex cones. We investigate the facial structure of a polyhedral cone C associated with a layered directed graph. A generalization of weak majorization based on C is introduced. It de nes a preorder of matrices. An application in statistical...

2003
Patrick J.F. Groenen Patrizia Giaquinto Henk A. L. Kiers Anton Béguin

For many least-squares decomposition models efficient algorithms are well known. A more difficult problem arises in decomposition models where each residual is weighted by a nonnegative value. A special case is principal components analysis with missing data. Kiers (1997) discusses an algorithm for minimizing weighted decomposition models by iterative majorization. In this paper, we propose a m...

2017
Naveed Latif Ðilda Pečarić Josip Pečarić

In this paper we show how the Shannon entropy is connected to the theory of majorization. They are both linked to the measure of disorder in a system. However, the theory of majorization usually gives stronger criteria than the entropic inequalities. We give some generalized results for majorization inequality using Csiszár f-divergence. This divergence, applied to some special convex functions...

2005
Francisco D. Martínez Pedro G. Massey Luis E. Silvestre

Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = Y, and consider the relations between this concept, strong majorization ( s ) and directional majorization ( ). It is verified that s⇒ ⇒ w , but none of the reciprocal implications is true. Nevertheless, we study the i...

Journal: :Linear Algebra and its Applications 2001

Journal: :Discrete Mathematics 2013
Richard A. Brualdi Geir Dahl

We generalize the classical notion of majorization in Rn to a majorization order for functions defined on a partially ordered set P . In this generalization we use inequalities for partial sums associated with ideals in P . Basic properties are established, including connections to classical majorization. Moreover, we investigate transfers (given by doubly stochastic matrices), complexity issue...

2006
MICHAEL G. NEUBAUER Michael G. Neubauer William Watkins

We introduce a partial order, variance majorization, on R, which is analogous to the majorization order. A new class of monotonicity inequalities, based on variance majorization and analogous to Schur convexity, is developed.

2008
CHRISTOPHER C. PAIGE

Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...

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