منابع مشابه
Parallel Reduction from Block Hessenberg to Hessenberg using MPI
In many scientific applications, eigenvalues of a matrix have to be computed. By first reducing a matrix from fully dense to Hessenberg form, eigenvalue computations with the QR algorithm become more efficient. Previous work on shared memory architectures has shown that the Hessenberg reduction is in some cases most efficient when performed in two stages: First reduce the matrix to block Hessen...
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Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety which arise in the study of quantum cohomology, geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent Hessenberg varieties for all classical types. This paving is in fact the intersection of a particular Bruhat decomposition with the Hes...
متن کاملHessenberg Input Normal Representations
Every stable controllable input pair (Ã , B̃ ) is equivalent to an input pair which is in Hessenberg form and is input normal (AA∗ + BB∗ = I ). (A,B) is represented as a submatrix of the minimal number of Givens rotations. The representation is shown to be generically identifiable. This canonical form allows for fast state vector updates and improved conditioning of system identification problem...
متن کاملThe Thin Set Theorem for Pairs Implies DNR
Answering a question in the reverse mathematics of combinatorial principles, we prove that the Thin Set Theorem for Pairs (TS(2)) implies the Diagonally NonComputable Set Principle (DNR) over the base axiom system RCA0. 1. BACKGROUND AND DEFINITIONS The reverse mathematics of combinatorial principles has generated a good amount of interest in recent years. In particular, a lot of principles hav...
متن کاملHessenberg Varieties and Hyperplane Arrangements
Given a semisimple complex linear algebraic group G and a lower ideal I in positive roots of G, three objects arise: the ideal arrangement AI , the regular nilpotent Hessenberg variety Hess(N, I), and the regular semisimple Hessenberg variety Hess(S, I). We show that a certain graded ring derived from the logarithmic derivation module of AI is isomorphic to H∗(Hess(N, I)) and H∗(Hess(S, I)) , t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.01.013