Multidimensional Problems

2005 ◽  
pp. 271-292
Keyword(s):  
Multidimensional Problems

Interpolation and extrapolation

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Public Transportation ◽  
Spline Interpolation ◽  
Lattice Gauge Theory ◽  
Human Vision ◽  
Physical Sciences ◽  
One Dimensional ◽  
Lattice Gauge ◽  
Multidimensional Problems ◽  
Data Points ◽  
Lagrange Interpolating Polynomial

This chapter deals with two related problems occurring frequently in the physical sciences: first, the problem of estimating the value of a function from a limited number of data points; and second, the problem of calculating its value from a series approximation. Numerical methods for interpolating and extrapolating data are presented. The famous Lagrange interpolating polynomial is introduced and applied to one-dimensional and multidimensional problems. Cubic spline interpolation is introduced and an implementation in terms of Eigen classes is given. Several techniques for improving the convergence of Taylor series are discussed, including Shank’s transformation, Richardson extrapolation, and the use of Padé approximants. Conversion between representations with the quotient-difference algorithm is discussed. The exercises explore public transportation, human vision, the wine market, and SU(2) lattice gauge theory, among other topics.

Multidimensional Problems

1981 ◽  
pp. 127-154
Author(s):  
LEON COOPER ◽  
MARY W. COOPER
Keyword(s):  
Multidimensional Problems

scholarly journals Change in multidimensional problems and quality of life over three months after HIV diagnosis: a multicentre longitudinal study in Kenya and Uganda

2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Victoria Simms ◽  
Julia Downing ◽  
Eve Namisango ◽  
R. Anthony Powell ◽  
Faith Mwangi-Powell ◽  
...  
Keyword(s):  
Quality Of Life ◽  
Longitudinal Study ◽  
Hiv Diagnosis ◽  
Multidimensional Problems

Incomplete Iterative Implicit Schemes

2020 ◽  
Vol 20 (4) ◽  
pp. 727-737 ◽  
Author(s):  
Petr N. Vabishchevich
Keyword(s):  
Approximate Solution ◽  
Iterative Methods ◽  
Parabolic Equations ◽  
Evolutionary Equation ◽  
Finite Dimensional ◽  
Implicit Schemes ◽  
Multidimensional Problems ◽  
Computational Implementation ◽  
The Stability ◽  
Finite Dimensional Hilbert Space

AbstractIn numerical solving boundary value problems for parabolic equations, two- or three-level implicit schemes are in common use. Their computational implementation is based on solving a discrete elliptic problem at a new time level. For this purpose, various iterative methods are applied to multidimensional problems evaluating an approximate solution with some error. It is necessary to ensure that these errors do not violate the stability of the approximate solution, i.e., the approximate solution must converge to the exact one. In the present paper, these questions are investigated in numerical solving a Cauchy problem for a linear evolutionary equation of first order, which is considered in a finite-dimensional Hilbert space. The study is based on the general theory of stability (well-posedness) of operator-difference schemes developed by Samarskii. The iterative methods used in the study are considered from the same general positions.

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