Related papers: Finite Gap Jacobi Matrices: A Review

Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.

Jacobi-type iterative algorithms for the eigenvalue decomposition, singular value decomposition, and Takagi factorization of complex matrices are presented. They are implemented as compact Fortran 77 subroutines in a freely available…

We introduce affine structures on groups and show they form a category equivalent to that of semi-braces. In particular, such a new description of semi-braces includes that presented by Rump for braces. By specific affine structures, we…

We shall realize certain affine geometric crystal of type $G^{(1)}_2$ explicitly in the fundamental representation $W(\varpi_1)$. Its explicit form is rather complicated but still keeps a positive structure.

Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.

Szmytkowski derived a certain integral with Gegenbauer polynomials. A natural generalization is to derive lookalike integrals with Jacobi polynomials. Six methods are treated to derive the first integral. The first method should be enough…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

We give a survey of the analytic theory of matrix orthogonal polynomials.

I review and discuss a selected sample of recent results in pNRQCD.

This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.

The Jacobian Conjecture would follow if it were known that real polynomial maps with a unipotent Jacobian matrix are injective. The conjecture that this is true even for $C^1$ maps is explored here. Some results known in the polynomial case…

We outline a new approach to classify real forms and automorphisms of finite order of affine Kac-Moody algebras.

The essential elements in my way of fitting the kappa reviewed. A number of incorrect claims made by Takamatsu are clarified and corrected.

Comment on ``Gibbs Sampling, Exponential Families and Orthogonal Polynomials'' [arXiv:0808.3852]

We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.

We use Matrix Analysis to prove a general decoupling inequality for finite Gaussian vectors, in identifying a new region of the inherent $p$ exponent, for the validity of this one.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

The eigenvalue problem is a fundamental problem in scientific computing. In this paper, we first give the error analysis for a single step or sweep of Jacobi's method in floating point arithmetic. Then we propose a mixed precision…