Convergence

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Convergence is the approach toward a definite value, a definite point, a common view or opinion, or toward a fixed or equilibrium state. In mathematics, it describes limiting behavior, particularly of an infinite sequence or series. Convergence, convergent, or converge may refer to:

Mathematics

• Limit (mathematics), refers generally to the notion that certain objects are approaching a limit in some sense
• Convergent series, a sequence of which the partial sums have a limit
• Convergent (continued fraction) of a (possibly infinite) continued fraction
• Convergent sequence, a sequence which has a limit

Modes of convergence

• Modes of convergence
• Absolute convergence pertains to whether the absolute value of the limit of a series or integral is finite.
• Uniform convergence, a pointwise convergence where the speed of convergence is independent of any value in the domain
• Pointwise convergence, the convergence of functions' values at each specific input individually

convergence theory

Properties of convergence

• Rate of convergence, the "speed" at which a convergent sequence approaches its limit
• Radius of convergence, a non-negative quantity that represents a domain interval over which a power series converges

Theorems and notions about convergence

• Convergence of random variables, any one of several notions of convergence in probability theory
• Gromov–Hausdorff convergence pertains to metric spaces and is a generalization of Hausdorff distance
• Dominated convergence theorem, a theorem by Henri Lebesgue
• Monotone convergence theorem, any one of several such theorems defined over a monotone sequence of numbers

Generalizations and applications

• Convergence of Fourier series pertains to whether the Fourier series of a periodic function converges
• Net (mathematics), or "convergent net", a generalization of a convergent sequence
• Filter (mathematics), or "convergent filter", a generalization of a convergent net
• Convergence of a numerical method, for solving differential equations
• Integral test for convergence , a technique used to test infinite series of nonnegative terms for convergence

Natural sciences

• Convergence (eye), simultaneous inward movement of eyes toward each other
• Convergent evolution, a process by which unrelated organisms independently acquire similar characteristics while evolving in separate 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

Computing and technology

• 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
• Converge (programming language)
• 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
• Technological convergence, a trend where some technologies having distinct functionalities evolve to technologies that overlap

Social sciences

• Language convergence, the blending of two languages that are perceived as having equal social status
• Catch-up effect, in economic theory, otherwise known as the "theory of convergence"
• Technological convergence, the removal of entry barriers across the IT, telecoms, media and consumer electronics industries
• Convergent and divergent production, two types of human response to a set problem

Society and culture

Entertainment

Literature

• Convergence (series), edited by Ruth Nanda Anshen
• Convergence (novel), by Charles Sheffield
• The Pendragon Adventure, a book series in which the main threat is of Convergence

Music

• Converge (band), a band from Massachusetts
• Convergence (album), by James Murphy
• Convergence (Dave Douglas album)

Politics

• Convergence (Mexico), a political party in Mexico
• Democratic Convergence Party (Cape Verde)
• Democratic Convergence Party-Reflection Group in São Tomé and Príncipe
• Democratic Convergence of Catalonia, a political party in Catalonia, Spain
  • Convergence and Union, a coalition of two political parties in Catalonia, Spain
• Convergence for Social Democracy, a political party in Equatorial Guinea
• National Convergence, a political party in Venezuela
• Anti-Capitalist Convergence, a group of political organizations

Gatherings

• Convergence (goth festival)
• CONvergence (convention), a speculative fiction convention in Minnesota
• Convergence (Net-25 program), a premier IT Show on Net 25 in the Philippines

Other

• Harmonic Convergence, a new age spiritual event in 1987

See also

• Divergence (disambiguation)

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