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28 relations: Approximation theory, Boundary value problem, David M. Young Jr., Differential equation, Discretization, Elliptic partial differential equation, Finite difference, Gauss–Seidel method, Interpolation, Iterative method, Jacobi method, Laplace's equation, Linear least squares (mathematics), Linear programming, Linear system, Mathematical optimization, Multigrid method, Numerical analysis, Poisson's equation, Preconditioner, Relaxation (approximation), Richard S. Varga, Smoothing, Society for Industrial and Applied Mathematics, Sparse matrix, Successive over-relaxation, System of equations, Yousef Saad.
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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David M. Young Jr.
David M. Young Jr. (October 20, 1923 – December 21, 2008) was an American mathematician and computer scientist who was one of the pioneers in the field of modern numerical analysis/scientific computing.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Discretization
In mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts.
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Elliptic partial differential equation
Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic.
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Finite difference
A finite difference is a mathematical expression of the form.
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Gauss–Seidel method
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
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Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
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Jacobi method
In numerical linear algebra, the Jacobi method (or Jacobi iterative method) is an algorithm for determining the solutions of a diagonally dominant system of linear equations.
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Laplace's equation
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
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Linear least squares (mathematics)
In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model.
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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Linear system
A linear system is a mathematical model of a system based on the use of a linear operator.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Multigrid method
Multigrid (MG) methods in numerical analysis are algorithms for solving differential equations using a hierarchy of discretizations.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics.
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Preconditioner
In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods.
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Relaxation (approximation)
In mathematical optimization and related fields, relaxation is a modeling strategy.
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Richard S. Varga
Richard Steven Varga (born October 9, 1928) is an American mathematician who specializes in numerical analysis and linear algebra.
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Smoothing
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena.
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Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.
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Sparse matrix
In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero.
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Successive over-relaxation
In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence.
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System of equations
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
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Yousef Saad
Yousef Saad is an I.T. Distinguished Professor of Computer Science in the Department of Computer Science and Engineering at the University of Minnesota.
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References
[1] https://en.wikipedia.org/wiki/Relaxation_(iterative_method)
