scholarly journals On recurrence coefficients for rapidly decreasing exponential weights

2007 ◽  
Vol 144 (2) ◽  
pp. 260-281 ◽  
Author(s):  
E. Levin ◽  
D.S. Lubinsky
Keyword(s):  
Exponential Weights ◽  
Recurrence Coefficients

scholarly journals Non-existence of bi-infinite geodesics in the exponential corner growth model

2020 ◽  
Vol 8 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Coarse Graining ◽  
Exponential Weights ◽  
Percolation Process ◽  
Last Passage Percolation ◽  
Corner Growth Model ◽  
And Control

Abstract This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

Orthogonal polynomials: applications and computation

Acta Numerica ◽  
1996 ◽  
Vol 5 ◽  
pp. 45-119 ◽  
Author(s):  
Walter Gautschi
Keyword(s):  
Numerical Methods ◽  
Weight Function ◽  
Orthogonal Polynomials ◽  
Rational Function ◽  
Recurrence Relations ◽  
Recurrence Coefficients ◽  
Basic Task ◽  
Sobolev Orthogonal Polynomials ◽  
Gauss Type ◽  
Three Term Recurrence Relation

We give examples of problem areas in interpolation, approximation, and quadrature, that call for orthogonal polynomials not of the classical kind. We then discuss numerical methods of computing the respective Gauss-type quadrature rules and orthogonal polynomials. The basic task is to compute the coefficients in the three-term recurrence relation for the orthogonal polynomials. This can be done by methods relying either on moment information or on discretization procedures. The effect on the recurrence coefficients of multiplying the weight function by a rational function is also discussed. Similar methods are applicable to computing Sobolev orthogonal polynomials, although their recurrence relations are more complicated. The paper concludes with a brief account of available software.

Sign in / Sign up

Export Citation Format

Share Document