L1 Approximation with Bounded Variables

Chapman & Hall/CRC Numerical Analy & Scient Comp. Series - Numerical Linear Approximation in C ◽

10.1201/9781584889793.ch7 ◽

2008 ◽

pp. 213-244

Keyword(s):

Bounded Variables ◽

L1 Approximation

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

Advances in Difference Equations ◽

10.1186/s13662-020-03178-8 ◽

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.

An explicit solution of an L1 approximation problem

Journal of Approximation Theory ◽

10.1016/0021-9045(85)90082-6 ◽

1985 ◽

Vol 44 (2) ◽

pp. 194-195

Author(s):

D Kershaw

Keyword(s):

Explicit Solution ◽

Approximation Problem ◽

L1 Approximation

Properties of unicity subspaces in L1-approximation

Journal of Approximation Theory ◽

10.1016/0021-9045(88)90042-1 ◽

1988 ◽

Vol 52 (3) ◽

pp. 269-283 ◽

Cited By ~ 2

Author(s):

Manfred Sommer

Keyword(s):

L1 Approximation

One sided L1-approximation as a problem of semi-infinite linear programming

Semi-Infinite Programming - Lecture Notes in Control and Information Sciences ◽

10.1007/bfb0003891 ◽

2005 ◽

pp. 173-178

Author(s):

W. Krabs

Keyword(s):

Linear Programming ◽

Infinite Linear Programming ◽

L1 Approximation ◽

Infinite Linear

An example of L1 approximation and the discrete case

Approximation Theory and Methods ◽

10.1017/cbo9781139171502.016 ◽

1981 ◽

pp. 177-188

Keyword(s):

Discrete Case ◽

L1 Approximation

The natural best L1-approximation by nondecreasing functions

Journal of Approximation Theory ◽

10.1016/0021-9045(88)90052-4 ◽

1988 ◽

Vol 52 (2) ◽

pp. 132-140 ◽

Cited By ~ 9

Author(s):

Robert Huotari ◽

David Legg ◽

Aaron D Meyerowitz ◽

Douglas Townsend

Keyword(s):

L1 Approximation ◽

Nondecreasing Functions

Weighted median algorithms for L1 approximation

BIT Numerical Mathematics ◽

10.1007/bf02017350 ◽

1990 ◽

Vol 30 (2) ◽

pp. 301-310 ◽

Cited By ~ 18

Author(s):

Chaya Gurwitz

Keyword(s):

L1 Approximation ◽

Weighted Median

Chebyshev and L1solutions of overdetermined systems of linear equations with bounded variables

Numerical Functional Analysis and Optimization ◽

10.1080/01630568608816220 ◽

1986 ◽

Vol 8 (3-4) ◽

pp. 399-418 ◽

Cited By ~ 1

Author(s):

Nabih N. Abdelmalek

Keyword(s):

Linear Equations ◽

Overdetermined Systems ◽

Bounded Variables ◽

Systems Of Linear Equations

Transformation of Bounded Variables in Simplex Optimization Techniques

Industrial & Engineering Chemistry Process Design and Development ◽

10.1021/i260048a019 ◽

1973 ◽

Vol 12 (4) ◽

pp. 485-486 ◽

Cited By ~ 6

Author(s):

G. Richard Atwood ◽

William W. Foster

Keyword(s):

Optimization Techniques ◽

Simplex Optimization ◽

Bounded Variables