Exact convergence rates for best L P rational approximation to the signum function and for optimal quadrature in H P

1993 ◽  
pp. 98-109
Author(s):  
A. L. Levin ◽  
E. B. Saff
Keyword(s):  
Rational Approximation ◽  
Convergence Rates ◽  
Optimal Quadrature ◽  
Signum Function

scholarly journals On Rational Krylov and Reduced Basis Methods for Fractional Diffusion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tobias Danczul ◽  
Clemens Hofreither
Keyword(s):  
Rational Approximation ◽  
Convergence Rates ◽  
Fractional Diffusion ◽  
Point Of View ◽  
Spectral Interval ◽  
Krylov Methods ◽  
Reduced Basis ◽  
Reduced Basis Methods ◽  
Approximation Classes ◽  
Diffusion Problems

Abstract We establish an equivalence between two classes of methods for solving fractional diffusion problems, namely, Reduced Basis Methods (RBM) and Rational Krylov Methods (RKM). In particular, we demonstrate that several recently proposed RBMs for fractional diffusion can be interpreted as RKMs. This changed point of view allows us to give convergence proofs for some methods where none were previously available. We also propose a new RKM for fractional diffusion problems with poles chosen using the best rational approximation of the function 𝑧 −𝑠 with 𝑧 ranging over the spectral interval of the spatial discretization matrix. We prove convergence rates for this method and demonstrate numerically that it is competitive with or superior to many methods from the reduced basis, rational Krylov, and direct rational approximation classes. We provide numerical tests for some elliptic fractional diffusion model problems.

scholarly journals Convergence rates for inverse-free rational approximation of matrix functions

2016 ◽  
Vol 510 ◽  
pp. 291-310
Author(s):  
Carl Jagels ◽  
Thomas Mach ◽  
Lothar Reichel ◽  
Raf Vandebril
Keyword(s):  
Rational Approximation ◽  
Convergence Rates ◽  
Matrix Functions

Rational Approximation of Real Functions

1988 ◽  
Author(s):  
P. P. Petrushev ◽  
Vasil Atanasov Popov
Keyword(s):  
Rational Approximation ◽  
Real Functions

THE CONVERGENCE RATES OF ASYMPTOTICALLY BAYES DISCRIMINATION

1985 ◽  
Vol 5 (1) ◽  
pp. 67-78
Author(s):  
Laisheng Wei
Keyword(s):  
Convergence Rates

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

Müntz Rational Approximation in Orlicz Spaces

2012 ◽  
Vol 14 (1) ◽  
pp. 55
Author(s):  
Xiaohong WU ◽  
Garidi WU
Keyword(s):  
Rational Approximation ◽  
Orlicz Spaces
Sign in / Sign up

Export Citation Format

Share Document