Results 21 to 30 of about 26,182 (287)
Approximating the Largest Root and Applications to Interlacing Families [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2017 We study the problem of approximating the largest root of a real-rooted polynomial of degree $n$ using its top $k$ coefficients and give nearly matching upper and lower bounds. We present algorithms with running time polynomial in $k$ that use the top $k$
Nima Anari +3 more
semanticscholar +1 more source
The interesting spectral interlacing property for a certain tridiagonal matrix
, 2020 In this paper, a new tridiagonal matrix, whose eigenvalues are the same as the Sylvester-Kac matrix of the same order, is provided. The interest of this matrix relies also in that the spectrum of a principal submatrix is also of a Sylvester-Kac matrix ...
Carlos M. da Fonseca +2 more
semanticscholar +1 more source
Some Observations on the Smallest Adjacency Eigenvalue of a Graph
Discussiones Mathematicae Graph Theory, 2020 In this paper, we discuss various connections between the smallest eigenvalue of the adjacency matrix of a graph and its structure. There are several techniques for obtaining upper bounds on the smallest eigenvalue, and some of them are based on Rayleigh
Cioabă Sebastian M. +2 more
doaj +1 more source
A converse of Sturm's separation theorem
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a turning point in the principal part ...
Leila Gholizadeh, Angelo Mingarelli
doaj +1 more source
Dynamics of interlacing peakons (and shockpeakons) in the Geng-Xue equation [PDF]
, 2016 We consider multipeakon solutions, and to some extent also multishockpeakon solutions, of a coupled two-component integrable PDE found by Geng and Xue as a generalization of Novikov's cubically nonlinear Camassa-Holm type equation. In order to make sense
Hans Lundmark, J. Szmigielski
semanticscholar +1 more source
ISPRS International Journal of Geo-Information, 2021 Suitable graphic documentation is essential to ascertain and conserve architectural heritage. For the first time, accurate digital images are provided of a 16th-century wooden ceiling, composed of geometric interlacing patterns, in the Pinelo Palace in ...
Juan Francisco Reinoso-Gordo +2 more
doaj +1 more source
Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle [PDF]
, 2017 The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle.
K. Castillo, J. Petronilho
semanticscholar +1 more source
Variational characterizations for eigenfunctions of analytic self-adjoint operator functions [PDF]
Opuscula Mathematica, 2013 In this paper we consider Rellich's diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements.
Georgios Katsouleas, John Maroulas
doaj +1 more source
Interlacing Ehrhart polynomials of reflexive polytopes [PDF]
, 2016 It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties shared by the Riemann $$\zeta $$ζ function. The construction was generalized by Matsui et al. to a larger family of reflexive polytopes coming from graphs.
A. Higashitani +2 more
semanticscholar +1 more source
Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2013 We prove that there exist infinite families of regular bipartite Ramanujan graphs of every degree bigger than 2. We do this by proving a variant of a conjecture of Bilu and Linial about the existence of good 2-lifts of every graph.
A. Marcus, D. Spielman, N. Srivastava
semanticscholar +1 more source