Convergence

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In the absence of a more specific context, convergence denotes the approach toward a definite value, as time goes on; or to a definite point, a common view or opinion, or toward a fixed or equilibrium state. Convergent is the adjectival form, and also a noun meaning an iterative approximation.

Contents 1 Mathematics 2 Natural sciences 3 Computing and technology 4 Marketing convergence 5 Social sciences 6 See also

[edit] Mathematics

In mathematics, convergence describes limiting behaviour, particularly of an infinite sequence or series, toward some limit. To assert convergence is to claim the existence of such a limit, which may be itself unknown. For any fixed standard of accuracy, however, you can always be sure to be within that limit, provided you have gone far enough. The following lists more specific usages of this word:

• Modes of convergence
• Convergent sequence, a sequence which has a limit; see limit of a sequence
• Convergent series, a sequence of which the partial sums have a limit
• Convergent (continued fraction) of a (possibly infinite) continued fraction
• Convergent net, a generalization of a convergent sequence
• Convergent filter, a generalization of a convergent net
• Integral test for convergence , a technique used to test infinite series of nonnegative terms for convergence
• Radius of convergence, a non-negative quantity that represents a domain interval over which a power series converges
• Uniform convergence, a pointwise convergence where the speed of convergence is independent of any value in the domain
• Monotone convergence theorem, any one of several such theorems defined over a monotone sequence of numbers
• Convergence of random variables, any one of several notions of convergence in probability theory
• Rate of convergence, the "speed" at which a convergent sequence approaches its limit
• Absolute convergence pertains to whether the absolute value of the limit of a series or integral is finite.
• Pointwise convergence, the convergence of functions' values at each specific input individually
• Gromov-Hausdorff convergence pertains to metric spaces and is a generalization of Hausdorff distance
• Convergence of Fourier series pertains to whether the Fourier series of a periodic function converges. Also known as classic harmonic analysis.
• Dominated convergence theorem, a theorem by Henri Lebesgue
• Convergence of a numerical method, for solving differential equations

The opposite of convergence is divergence. Divergence may be some kind of oscillation, unrestricted growth (recognised as the case of an infinite limit), or chaotic behavior. An infinite series that is divergent cannot be used for meaningful computations of its value. Nevertheless, divergent series can be summed formally, as generating functions or asymptotic series, or via some summation method.

[edit] Natural sciences

• Convergent evolution pertains to organisms not closely related that independently acquire similar characteristics while evolving in separate and sometimes varying ecosystems.
• Convergent synthesis, a strategy that aims to improve the efficiency of multi-step chemical synthesis
• Convergent boundary, a fault boundary defined in the specialty of geology known as plate tectonics
• Convergence zone, in meteorology, an area where the horizontal wind produces a net in-flow of air
  • South Pacific convergence zone, a belt of low pressure from the west Pacific warm pool
  • Intertropical convergence zone, a belt of low pressure at the equator.
• Convergence (eye), the simultaneous inward movement of both eyes toward each other

[edit] Computing and technology

• Technological convergence, a trend where some technologies having distinct functionalities evolve to technologies that overlap
• Convergence (telecommunications), the combination of multiple services through lines of telecommunication from a single provider
• Convergence (routing protocol), the updating of routers' topography information using dynamic protocols
• Convergence (evolutionary computing), a means of modeling the tendency for genetic characteristics of populations to stabilize over time
• Premature convergence, an anomaly in evolutionary computation in which the population evolved to some stable yet sub-optimal state

[edit] Marketing convergence

• Marketing convergence, a trend where both offline and online marketing techniques evolve to methodologies that overlap

[edit] Social sciences

• Language convergence, the blending of two languages that are perceived as having equal social status; opposite of non-convergent discourse
• Non-convergent discourse, the persistence of asymmetric or bilingual discourse in natural languages
• Catch-up effect, in economic theory, otherwise known as the theory of convergence
• Convergence criteria, requirements specified by the European Union that stipulate the membership qualifications each state must fulfill
• Media convergence, the removal of entry barriers across the IT, telecoms, media and consumer electronics industries, creating one large "converged" industry
• Telecommunication convergence, a marketing concept with heavy technological implications
• Futures and cash market price convergence, the tendency of the futures price and cash price at the delivery location to come together as the delivery period approaches

[edit] See also

• Divergence (disambiguation)

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