Estimating the error in matrix function approximations

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Nasim Eshghi ◽  
Lothar Reichel
Keyword(s):  
Matrix Function ◽  
Function Approximations

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

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

Critical correlation-function approximations for the Ising model

1978 ◽  
Vol 11 (10) ◽  
pp. 2087-2093 ◽  
Author(s):  
B Frank ◽  
O Mitran
Keyword(s):  
Correlation Function ◽  
Ising Model ◽  
Function Approximations

P -Function Approximations for Jet Momentum Flux

1972 ◽  
Vol 98 (4) ◽  
pp. 1011-1016
Author(s):  
W. Hall C. Maxwell ◽  
Kuo-Cheng Chang
Keyword(s):  
Momentum Flux ◽  
Function Approximations

The solution of theoretical seismic problems by best rational function approximations for Laplace transform inversion

1975 ◽  
Vol 65 (4) ◽  
pp. 927-935
Author(s):  
I. M. Longman ◽  
T. Beer
Keyword(s):  
Laplace Transform ◽  
Rational Function ◽  
High Accuracy ◽  
Time Variable ◽  
Inversion Method ◽  
The Laplace Transform ◽  
Previously Treated ◽  
The Mean ◽  
Function Approximations ◽  
Laplace Transform Inversion

Abstract In a recent paper, the first author has developed a method of computation of “best” rational function approximations ḡn(p) to a given function f̄(p) of the Laplace transform operator p. These approximations are best in the sense that analytic inversion of ḡn(p) gives a function gn(t) of the time variable t, which approximates the (generally unknown) inverse f(t) of f̄(p in a minimum least-squares manner. Only f̄(p) but not f(t) is required to be known in order to carry out this process. n is the “order” of the approximation, and it can be shown that as n tends to infinity gn(t) tends to f(t) in the mean. Under suitable conditions on f(t) the convergence is extremely rapid, and quite low values of n (four or five, say) are sufficient to give high accuracy for all t ≧ 0. For seismological applications, we use geometrical optics to subtract out of f(t) its discontinuities, and bring it to a form in which the above inversion method is very rapidly convergent. This modification is of course carried out (suitably transformed) on f̄(p), and the discontinuities are restored to f(t) after the inversion. An application is given to an example previously treated by the first author by a different method, and it is a certain vindication of the present method that an error in the previously given solution is brought to light. The paper also presents a new analytical method for handling the Bessel function integrals that occur in theoretical seismic problems related to layered media.

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