scholarly journals Eigenvalue problems for a class of infinite complex symmetric tridiagonal matrices with related three-term recurrence relation

2021 ◽  
pp. 113964
Author(s):  
Nobuyoshi Asai ◽  
Yoshinori Miyazaki
Keyword(s):  
Recurrence Relation ◽  
Eigenvalue Problems ◽  
Tridiagonal Matrices ◽  
Complex Symmetric ◽  
Three Term Recurrence Relation

scholarly journals On a quaternionic sequence with Vietoris’ numbers

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1065-1086
Author(s):  
P. Catarino ◽  
Almeida de
Keyword(s):  
Recurrence Relation ◽  
Generating Function ◽  
Type Formula ◽  
Tridiagonal Matrices ◽  
Three Term Recurrence Relation ◽  
Rational Sequence

Special integers sequences have been the center of attention for many researchers, as well as the sequences of quaternions where its components are the elements of these sequences. Motivated by a rational sequence, we consider the quaternions with components Vietoris? numbers and investigate some of its properties. For this sequence a two and three term recurrence relation is established, as well as a Binet?s type formula. Moreover the generating function for this sequence is introduced and also the determinant of some tridiagonal matrices are used in order to find elements of this sequence.

scholarly journals An ubiquitous three-term recurrence relation

2021 ◽  
Vol 62 (3) ◽  
pp. 032106
Author(s):  
Paolo Amore ◽  
Francisco M. Fernández
Keyword(s):  
Recurrence Relation ◽  
Three Term Recurrence Relation

scholarly journals On hypergeometric generalized negative binomial distribution

2002 ◽  
Vol 29 (12) ◽  
pp. 727-736 ◽  
Author(s):  
M. E. Ghitany ◽  
S. A. Al-Awadhi ◽  
S. L. Kalla
Keyword(s):  
Recurrence Relation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Field Data ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Generalized Negative Binomial Distribution ◽  
The Right ◽  
Three Term Recurrence Relation

It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated.

scholarly journals On the three term recurrence relation and BDF methods

2020 ◽  
Author(s):  
Larissa Ferreira Marques ◽  
Vanessa Botta ◽  
Messias Meneguette
Keyword(s):  
Recurrence Relation ◽  
Bdf Methods ◽  
Three Term Recurrence Relation

scholarly journals ELEMENTARY OSCILLATION CRITERIA FOR A THREE TERM RECURRENCE RELATION WITH OSCILLATORY COEFFICIENT SEQUENCE

1998 ◽  
Vol 29 (3) ◽  
pp. 227-232
Author(s):  
GUANG ZHANG ◽  
SUI-SUN CHENG
Keyword(s):  
Recurrence Relation ◽  
Recurrence Relations ◽  
Qualitative Properties ◽  
Oscillation Criteria ◽  
Three Term Recurrence Relation

Qualitative properties of recurrence relations with coefficients taking on both positive and negative values are difficult to obtain since mathematical tools are scarce. In this note we start from scratch and obtain a number of oscillation criteria for one such relation : $x_{n+1}-x_n+p_nx_{n-r}\le 0$.

scholarly journals Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I

2020 ◽  
Author(s):  
Grzegorz Świderski ◽  
Bartosz Trojan
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Behaviour ◽  
Recurrence Relation ◽  
Scaling Limits ◽  
Christoffel Functions ◽  
Asymptotically Periodic ◽  
Three Term Recurrence Relation

Abstract For Jacobi parameters belonging to one of three classes: asymptotically periodic, periodically modulated, and the blend of these two, we study the asymptotic behavior of the Christoffel functions and the scaling limits of the Christoffel–Darboux kernel. We assume regularity of Jacobi parameters in terms of the Stolz class. We emphasize that the first class only gives rise to measures with compact supports.

A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Cun-Qiang Miao
Keyword(s):  
Convergence Rate ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Eigenvalue Problems ◽  
Cubic Convergence ◽  
Davidson Method ◽  
Filtering Technique ◽  
Matrix Vector ◽  
Three Term Recurrence Relation ◽  
Symmetric Eigenvalue Problems

AbstractFor symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.

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