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Condition numbers of Hessenberg companion matrices
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of...
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Which Schubert Varieties are Hessenberg Varieties?
After proving that every Schubert variety in the full flag variety of a complex reductive group G is a general Hessenberg variety, we show that not...
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Perverse Sheaves and the Cohomology of Regular Hessenberg Varieties
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot action of...
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Comparison theorems for splittings of M-matrices in (block) Hessenberg form
Some variants of the (block) Gauss–Seidel iteration for the solution of linear systems with M -matrices in (block) Hessenberg form are discussed....
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AN ADDITIVE BASIS FOR THE COHOMOLOGY RINGS OF REGULAR NILPOTENT HESSENBERG VARIETIES
In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all...
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Geometric Vertex Decomposition, Gröbner Bases, and Frobenius Splittings for Regular Nilpotent Hessenberg Varieties
We initiate a study of the Gröbner geometry of local defining ideals of Hessenberg varieties by studying the special case of regular nilpotent...
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Projection schemes based on Hessenberg process for Sylvester tensor equation with low-rank right-hand side
In this paper, we present two new projection methods based on the Hessenberg process to compute the approximate solutions of Sylvester tensor...
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Discontinuous piecewise polynomial collocation methods for integral-algebraic equations of Hessenberg type
This paper mainly focuses on the integral-algebraic equations (IAEs) of Hessenberg type. The tractability index is investigated. The existence,...
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The Second Cohomology of Regular Semisimple Hessenberg Varieties from GKM Theory
AbstractWe describe the second cohomology of a regular semisimple Hessenberg variety by generators and relations explicitly in terms of GKM theory....
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Hessenberg varieties of parabolic type
This paper studies the geometry and combinatorics of three interrelated varieties: Springer fibers, Steinberg varieties, and parabolic Hessenberg...
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Toward Permutation Bases in the Equivariant Cohomology Rings of Regular Semisimple Hessenberg Varieties
Recent work of Shareshian and Wachs, Brosnan and Chow, and Guay-Paquet connects the well-known Stanley–Stembridge conjecture in combinatorics to the...
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Characteristic Polynomials of Random Banded Hessenberg Matrices and Hermite–Padé Approximation
We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions...
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A filtration on the cohomology rings of regular nilpotent Hessenberg varieties
Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent...
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On generating Sobolev orthogonal polynomials
Sobolev orthogonal polynomials are polynomials orthogonal with respect to a Sobolev inner product, an inner product in which derivatives of the...
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Convergence Acceleration of Shifted LR Transformations for Totally Nonnegative Hessenberg Matrices
We design shifted LR transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of...
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Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These...
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A Survey of Recent Developments on Hessenberg Varieties
This article surveys recent developments on Hessenberg varieties, emphasizing some of the rich connections of their cohomology and combinatorics. In...