scholarly journals New matrix function approximations and quadrature rules based on the Arnoldi process

2021 ◽  
Vol 391 ◽  
pp. 113442
Author(s):  
Nasim Eshghi ◽  
Thomas Mach ◽  
Lothar Reichel
Keyword(s):  
Matrix Function ◽  
Quadrature Rules ◽  
Arnoldi Process ◽  
Function Approximations

Quadrature Rules Based on the Arnoldi Process

2005 ◽  
Vol 26 (3) ◽  
pp. 765-781 ◽  
Author(s):  
Daniela Calvetti ◽  
Sun-Mi Kim ◽  
Lothar Reichel
Keyword(s):  
Quadrature Rules ◽  
Arnoldi Process

scholarly journals On Appel-Type Quadrature Rules

2002 ◽  
Vol 9 (3) ◽  
pp. 405-412
Author(s):  
C. Belingeri ◽  
B. Germano
Keyword(s):  
Remainder Term ◽  
Quadrature Rule ◽  
Bernoulli Numbers ◽  
Quadrature Rules ◽  
Rule Based ◽  
Numerical Example ◽  
The Given ◽  
Derivatives Of

Abstract The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the endpoints of the considered interval. In the general case, the remainder term is expressed in terms of Appel numbers, and all derivatives appear. A numerical example is also included.

Acoustic Green's Function Approximations

1998 ◽  
Vol 06 (04) ◽  
pp. 435-452 ◽  
Author(s):  
Robert P. Gilbert ◽  
Zhongyan Lin ◽  
Klaus Hackl
Keyword(s):  
Inverse Problem ◽  
Normal Mode ◽  
Eigenvalue Problems ◽  
Normal Modes ◽  
Modal Parameters ◽  
Mindlin Plate ◽  
Ocean Bottom ◽  
Hankel Transformation ◽  
Poroelastic Materials ◽  
Function Approximations

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

Dynamic Stability Analysis by Matrix Function

1987 ◽  
Vol 113 (7) ◽  
pp. 1085-1100 ◽  
Author(s):  
Tsunemi Shigematsu ◽  
Takashi Hara ◽  
Mitao Ohga
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Matrix Function
Sign in / Sign up

Export Citation Format

Share Document