نتایج جستجو برای: schur index

تعداد نتایج: 400323  

2005
Chris Siefert Eric de Sturler

Several Schur complement-based preconditioners have been proposed for solving (generalized) saddlepoint problems. We consider probing-based methods for approximating those Schur complements in the preconditioners of the type proposed by [Murphy, Golub and Wathen ’00], [de Sturler and Liesen ’03] and [Siefert and de Sturler ’04]. This approach can be applied in similar preconditioners as well. W...

Journal: :J. Comb. Theory, Ser. A 2009
Daniel Bravo Luc Lapointe

The Bernstein operators allow to build recursively the Schur functions. We present a recursion formula for k-Schur functions at t = 1 based on combinatorial operators that generalize the Bernstein operators. The recursion leads immediately to a combinatorial interpretation for the expansion coefficients of k-Schur functions at t = 1 in terms of homogeneous symmetric functions.

2017
Younseok Choo

This paper concerns the Schur stability of polynomials. Firstly necessary conditions are presented for the Schur stability of complex polynomials with fixed coefficients based on the discrete Hermite-Biehler theorem. Then the result is applied to obtain necessary conditions for the robust Schur stability of real interval polynomials.

2010
JIANZHOU LIU RONG HUANG

In this paper, we obtain some formulas for compound matrices of generalized Schur complements of matrices. Further, we give some Löwner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of Schur complements of sums of positive semidefinite Hermitian matrices.

2007
Jiping Liu Pablo Spiga Qiang Wang

In [HiMu] the authors, in their analysis on Schur rings, pointed out that it is not known whether there exists a non-Schurian p-Schur ring over an elementary abelian p-group of rank 3. In this paper we prove that every p-Schur ring over an elementary abelian p-group of rank 3 is in fact Schurian.

2011
FEDERICO ARDILA LUIS G. SERRANO Elizabeth Dewitt

We prove Stanley’s conjecture that, if δn is the staircase shape, then the skew Schur functions sδn/μ are non-negative sums of Schur P -functions. We prove that the coefficients in this sum count certain fillings of shifted shapes. In particular, for the skew Schur function sδn/δn−2 , we discuss connections with Eulerian numbers and alternating permutations.

Journal: :Eur. J. Comb. 2016
Vasu Tewari

We prove a Murnaghan-Nakayama rule for noncommutative Schur functions introduced by Bessenrodt, Luoto and van Willigenburg. In other words, we give an explicit combinatorial formula for expanding the product of a noncommutative power sum symmetric function and a noncommutative Schur function in terms of noncommutative Schur functions. In direct analogy to the classical Murnaghan-Nakayama rule, ...

2007
MIRJANA VULETIĆ M. VULETIĆ

In this paper we define the shifted Schur process as a measure on sequences of strict partitions. This process is a generalization of the shifted Schur measure introduced in [TW] and [Mat] and is a shifted version of the Schur process introduced in [OR1]. We prove that the shifted Schur process defines a Pfaffian point process. We further apply this fact to compute the bulk scaling limit of the...

2004
A. Bultheel A. Lasarow ADHEMAR BULTHEEL ANDREAS LASAROW

We study certain sequences of rational functions with poles outside the unit circle. Such kind of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur-Nevanlinna algorithm for Schur functions on the one hand and on the other hand to orthogonal rational functions on the unit circle. We shall ...

1998
Thierry Braconnier Yousef Saad

Computing the partial Schur form of a matrix is a common kernel in widely used software for solving eigenvalues problems. Partial Schur forms and Schur vectors also arise naturally in deeation techniques. In this paper, error bounds are proposed which are based on the Schur form of a matrix. We show how the bounds derived for the general case simplify in special situations such as those of Herm...

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