scholarly journals The natural best L1-approximation by nondecreasing functions

1988 ◽  
Vol 52 (2) ◽  
pp. 132-140 ◽  
Author(s):  
Robert Huotari ◽  
David Legg ◽  
Aaron D Meyerowitz ◽  
Douglas Townsend
Keyword(s):  
L1 Approximation ◽  
Nondecreasing Functions

scholarly journals Novel finite point approach for solving time-fractional convection-dominated diffusion equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaomin Liu ◽  
Muhammad Abbas ◽  
Honghong Yang ◽  
Xinqiang Qin ◽  
Tahir Nazir
Keyword(s):  
Variable Coefficients ◽  
Numerical Dispersion ◽  
Discrete Equation ◽  
Finite Point ◽  
Spatial Direction ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Tailored Finite Point Method ◽  
L1 Approximation ◽  
The Stability

AbstractIn this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical oscillation or excessive numerical dispersion caused by convection dominant. The stability of the scheme is verified by theoretical analysis. Finally, one-dimensional and two-dimensional numerical examples are presented to verify the efficiency of the method.

Weighted median algorithms for L1 approximation

1990 ◽  
Vol 30 (2) ◽  
pp. 301-310 ◽  
Author(s):  
Chaya Gurwitz
Keyword(s):  
L1 Approximation ◽  
Weighted Median

scholarly journals On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Jukkrit Daengsaen ◽  
Anchalee Khemphet
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Convergence Theorem ◽  
Computational Cost ◽  
Closed Intervals ◽  
Iteration Methods ◽  
Nondecreasing Functions ◽  
New Iterative Method

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.

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