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Rate of convergence

Index Rate of convergence

In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence. [1]

18 relations: Aitken's delta-squared process, Algorithmic efficiency, Big O notation, Discretization, Endre Süli, Golden ratio, Iterative method, Limit of a sequence, Michelle Schatzman, Numerical analysis, Numerical integration, Numerical methods for ordinary differential equations, Secant method, Sequence, Sequence transformation, Series acceleration, Springer Science+Business Media, Truncation error (numerical integration).

Aitken's delta-squared process

In numerical analysis, Aitken's delta-squared process or Aitken Extrapolation is a series acceleration method, used for accelerating the rate of convergence of a sequence.

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Algorithmic efficiency

In computer science, algorithmic efficiency is a property of an algorithm which relates to the number of computational resources used by the algorithm.

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Big O notation

Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.

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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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Endre Süli

Endre Süli (also, Endre Suli) is Professor of Numerical Analysis in the Mathematical Institute, University of Oxford, Fellow and Tutor in Mathematics at Worcester College, Oxford and Supernumerary Fellow of Linacre College, Oxford.

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Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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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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Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

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Michelle Schatzman

Michelle Schatzman (1949–2010) was a French mathematician, specializing in applied mathematics, who combined research as a CNRS research director and teaching as a professor at the Claude Bernard University Lyon 1.

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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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Numerical integration

In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.

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Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).

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Secant method

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method.

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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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Sequence transformation

In mathematics, a sequence transformation is an operator acting on a given space of sequences (a sequence space).

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Series acceleration

In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Truncation error (numerical integration)

Truncation errors in numerical integration are of two kinds.

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Convergence order, Convergence rate, Cubic convergence, Linear convergence, Order of convergence, Q-linear, Quadratic convergence, Quadratically convergent, R-linear, Speed of convergence, Sublinear convergence, Superlinear convergence.

References

[1] https://en.wikipedia.org/wiki/Rate_of_convergence

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