Extrapolation - Linear extrapolation. This means creating a tangent line at the end of the known data and extending it beyond that limit. A linear extrapolation will only provide good results when used to extend the graph of an approximately linear function. A linear extrapolation can be done easily with a ruler on a written graph or with a computer. Extrapolat ...

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Extrapolation, Extrapolation - Extrapolation methods, Extrapolation - Linear extrapolation, Extrapolation - Circular constant curvature extrapolation, Extrapolation - Conic extrapolation, Extrapolation - Polynomial extrapolation, Extrapolation - Quality of extrapolation, Extrapolation - Examples of extrapolation error, Extrapolation - Extrapolation in the complex plane

Read more here: » Extrapolation: Encyclopedia II - Extrapolation - Extrapolation methods

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Extrapolation, Extrapolation - Extrapolation methods, Extrapolation - Linear extrapolation, Extrapolation - Circular constant curvature extrapolation, Extrapolation - Conic extrapolation, Extrapolation - Polynomial extrapolation, Extrapolation - Quality of extrapolation, Extrapolation - Examples of extrapolation error, Extrapolation - Extrapolation in the complex plane

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An extrapolation's reliability is indicated by its prediction confidence interval, which often diverges to impossible values. Extrapolating beyond that range can lead to misleading results. For example, the death rate from a new disease may increase dramatically early on. If the graph of the death rate is then extrapolated linearly, it might appear that the entire human population will be dead from the disease in a short number of years. In reality, the death rate from a newly discovered disease may fall as the susceptible die off and ...

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Extrapolation, Extrapolation - Extrapolation methods, Extrapolation - Linear extrapolation, Extrapolation - Circular constant curvature extrapolation, Extrapolation - Conic extrapolation, Extrapolation - Polynomial extrapolation, Extrapolation - Quality of extrapolation, Extrapolation - Examples of extrapolation error, Extrapolation - Extrapolation in the complex plane

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In complex analysis, a problem of extrapolation may be converted into an interpolation problem by the change of variable z → 1/z. This transform exchanges the part of the complex plane inside the unit circle with the part of the complex plane outside of the unit circle. In particular, the compactification point at infinity is mapped to the origin and vice versa. Care must be taken with this transform however, since the original function may have had "features", for example poles and other sin ...

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Extrapolation, Extrapolation - Extrapolation methods, Extrapolation - Linear extrapolation, Extrapolation - Circular constant curvature extrapolation, Extrapolation - Conic extrapolation, Extrapolation - Polynomial extrapolation, Extrapolation - Quality of extrapolation, Extrapolation - Examples of extrapolation error, Extrapolation - Extrapolation in the complex plane

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There are several reasons for carrying out numerical integration. The integrand f may be known only at certain points, such as obtained by sampling. Some embedded systems and other computer applications may need numerical integration for this reason. A formula for the integrand may be known, but it may be difficult or impossible to find an antiderivative. An example of such an integrand is exp(-t2). It may be possible to find an antiderivative symbolically, but it may be easier to compute a numerical ap ...

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Numerical integration, Numerical integration - Reasons for numerical integration, Numerical integration - Methods for one-dimensional integrals, Numerical integration - Quadrature rules based on interpolating functions, Numerical integration - Adaptive algorithms, Numerical integration - Extrapolation methods, Numerical integration - Conservative a priori error estimation, Numerical integration - Multidimensional integrals, Numerical integration - Monte Carlo, Numerical integration - Sparse grids, Numerical integration - Software for numerical integration

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Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral. An important part of the analysis of any numerical integration method is to study the behavior of the approximation error as a function of the number of integrand evaluations. A method which yields a small error for a small number of evaluations is usually considered superior. Reducing the number of evaluations of the integrand reduces the number of arithmetic operations involved, and therefore reduces the total round-off error. Also ...

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Numerical integration, Numerical integration - Reasons for numerical integration, Numerical integration - Methods for one-dimensional integrals, Numerical integration - Quadrature rules based on interpolating functions, Numerical integration - Adaptive algorithms, Numerical integration - Extrapolation methods, Numerical integration - Conservative a priori error estimation, Numerical integration - Multidimensional integrals, Numerical integration - Monte Carlo, Numerical integration - Sparse grids, Numerical integration - Software for numerical integration

Read more here: » Numerical integration: Encyclopedia II - Numerical integration - Methods for one-dimensional integrals

Three elements existed and characterize the period: lords, vassals and fiefs. Feudalism is defined by how these three elements fit together. A lord was a noble who owned land. A vassal was a person who was loaned land by the lord. The land was known as a fief. In exchange for the fief, the vassal would provide military service to the lord. The obligations and relations between lord, vassal and fief form the basis of feudalism. Feudalism - Lords vassals and fiefs. Before a lord could grant land, or f ...

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Feudalism, Feudalism - What is feudalism?, Feudalism - Lords vassals and fiefs, Feudalism - Examples of feudalism, Feudalism - History of the term feudalism, Feudalism - Invention of feudalism, Feudalism - Feudalism in history, Feudalism - Historians on feudalism, Feudalism - Notes on feudalism, Feudalism - Origins of feudalism, Feudalism - Decline of feudalism, Feudalism - Did feudalism exist?, Feudalism - Cautions on use of term Feudalism, Feudalism - Extrapolations of the meaning of feudalism, Feudalism - Other feudal-like systems, Feudalism - Notes, Feudalism - External link, Feudalism - Bibliography

Read more here: » Feudalism: Encyclopedia II - Feudalism - What is feudalism?

Criticism of Mormonism is the criticism of the Latter Day Saint movement, especially of the largest and most prominent sect, the Church of Jesus Christ of Latter-day Saints ("LDS Church"). In their early years, Mormons encountered frequent conflict, which forced them to move westward, eventually settling in Utah. Even after establishing a community in Utah, criticism to plural marriage and other beliefs prompted the Utah War. Criticism of Mormonism have largely been for theological reasons. Many Christians criticize Mormon doct ...

Including:

Criticism of Mormonism - Historic criticism Criticism of Mormonism - Doctrinal criticism
Criticism of Mormonism - Correct disagreements on doctrine Criticism of Mormonism - Incorrect disagreements on doctrine
Criticism of Mormonism - Anti-Mormonism
Criticism of Mormonism - Fabricated References Criticism of Mormonism - Use of Secondary Sources Criticism of Mormonism - Sensationalized exaggeration Criticism of Mormonism - Bait and Switch Criticism of Mormonism - Secret Teachings Criticism of Mormonism - Disputed extrapolation
Criticism of Mormonism - Criticism by Former Members Criticism of Mormonism - Criticisms of Mormonism as contrary to Science Criticism of Mormonism - Apologetics Criticism of Mormonism - General Conference and Temple Open House Protests
Criticism of Mormonism - Themes of anti-Mormon protestors
Criticism of Mormonism - Organized criticism to Mormonism Criticism of Mormonism - Seminars to counter Mormon teachings Criticism of Mormonism - Intra-Utah Anti Mormonism

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In a linear conception of time, the future is the portion of the timeline that has yet to occur, i.e. the place in space-time where lie all events that still have not occurred. In this sense the future is opposed to the past (the set of moments and events that have already occurred) and the present (the set of events that are occurring now). Future - The meaning of the future to mankind. The future has always had a very special place in philosophy and, in general, in the human mind. This is true largely bec ...

Including:

Future - The meaning of the future to mankind Future - In grammar
Future - Future tense in English Future - Future tenses and periphrastic constructions in Romance languages

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In physics, absolute zero is a fundamental lower bound on the temperature of a macroscopic system. It is an infinite number of orders of magnitude below any attainable temperature. It is by definition unachievable (after all, T appears in the denominator of many equations of thermodynamics), but its existence as a limit has been inferred from extrapolation from observed physical phenomena and from kinetic theory. Today it is defined as the temperature at which all (classical mechanical) motion of particles would cease -- in fact even at absolute zero some sort of motion would remain (helium is predicte ...

Including:

Absolute zero - History Absolute zero - Kinetic theory Absolute zero - Cryogenics Absolute zero - Thermodynamics and Absolute Zero Absolute zero - Absolute temperature scales Absolute zero - Negative temperatures

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The celestial equator is a great circle on the imaginary celestial sphere, which is actually the plane of the terrestrial equator extended out into the universe (i.e., it could be constructed by extrapolating the Earth's equator until it touches the celestial sphere). The celestial equator is inclined by ~23.5°, with respect to the ecliptic plane; a result of axial tilt. Celestial objects near the celestial equator are visible worldwide, b ...

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Virtual history, also referred to as counterfactual history, is a form of history which attempts to answer "what if" questions. It seeks to explore history and historical processes from the point of view of extrapolating a position in which certain key historical events did not happen or had an outcome which was different to that which did in fact occur. Most historians regard counterfactual history as sometimes entertaining, but not meeting the standards of mainstream historical research due to its speculative nature. It shoul ...

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In order to better understand what the term feudalism means, it is helpful to see how it was defined and how it has been used since its seventeenth century creation. Feudalism - Invention of feudalism. The word feudalism was not a medieval term. It was invented by French and English lawyers in the 17th century to describe certain traditional obligations between members of the warrior aristocracy. The term first reached a popular and wide audience in Montesquieu's De L'Esprit des Lois (The Spirit of the Laws) in 1748. Since then it has been red ...

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Feudalism, Feudalism - What is feudalism?, Feudalism - Lords vassals and fiefs, Feudalism - Examples of feudalism, Feudalism - History of the term feudalism, Feudalism - Invention of feudalism, Feudalism - Feudalism in history, Feudalism - Historians on feudalism, Feudalism - Notes on feudalism, Feudalism - Origins of feudalism, Feudalism - Decline of feudalism, Feudalism - Did feudalism exist?, Feudalism - Cautions on use of term Feudalism, Feudalism - Extrapolations of the meaning of feudalism, Feudalism - Other feudal-like systems, Feudalism - Notes, Feudalism - External link, Feudalism - Bibliography

Read more here: » Feudalism: Encyclopedia II - Feudalism - History of the term feudalism

In physical cosmology, the Big Bang is the scientific theory that the Universe emerged from an enormously dense and hot state about 13.7 billion years ago. The Big Bang is a consequence of the observed Hubble's law velocities of distant galaxies that when taken together with the cosmological principle imply that space is expanding according to the Friedmann-Lemaître model of general relativity. Extrapolated into the past, these observations show that the Universe has expanded from a primeval state, in which all the matter and energy ...

Including:

Big Bang - History Big Bang - Overview Big Bang - Theoretical underpinnings Big Bang - Observational evidence
Big Bang - Hubble's law expansion Big Bang - Cosmic microwave background radiation Big Bang - Abundance of primordial elements Big Bang - Galactic evolution and distribution
Big Bang - Features issues and problems
Big Bang - Horizon problem Big Bang - Flatness problem Big Bang - Magnetic monopoles Big Bang - Baryon asymmetry Big Bang - Globular cluster age Big Bang - Dark matter Big Bang - Dark energy
Big Bang - The future according to the Big Bang theory Big Bang - Speculative physics beyond the Big Bang Big Bang - Philosophical and religious interpretations

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Feudalism - Origins of feudalism. Vassalage agreements similar to what would later develop into legalized medieval feudalism originated from the blending of ancient Roman and Germanic traditions. The Romans had a custom of patronage whereby a stronger patron would provide protection to a weaker client in exchange for gifts, political support and prestige. In the countryside of the later Empire, the reforms of Diocletian and his successors attempted to put certain jobs, notably farming, on an hereditary basis. As ...

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Feudalism, Feudalism - What is feudalism?, Feudalism - Lords vassals and fiefs, Feudalism - Examples of feudalism, Feudalism - History of the term feudalism, Feudalism - Invention of feudalism, Feudalism - Feudalism in history, Feudalism - Historians on feudalism, Feudalism - Notes on feudalism, Feudalism - Origins of feudalism, Feudalism - Decline of feudalism, Feudalism - Did feudalism exist?, Feudalism - Cautions on use of term Feudalism, Feudalism - Extrapolations of the meaning of feudalism, Feudalism - Other feudal-like systems, Feudalism - Notes, Feudalism - External link, Feudalism - Bibliography

Read more here: » Feudalism: Encyclopedia II - Feudalism - Notes on feudalism

In mainstream Christianity, a strong disagreement with the theology, beliefs and practices of the Mormon church is common, see Mormonism and Christianity. In many ways, this tension is unsurprising: Mormon founders argued that mainstream Christianity is significantly different from what Jesus and the Apostles intended. Mormons teach that the biblically prophesied Great Apostasy has happened and that the mainstream Christ ...

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Criticism of Mormonism, Criticism of Mormonism - Historic criticism, Criticism of Mormonism - Doctrinal criticism, Criticism of Mormonism - Correct disagreements on doctrine, Criticism of Mormonism - Incorrect disagreements on doctrine, Criticism of Mormonism - Anti-Mormonism, Criticism of Mormonism - Fabricated References, Criticism of Mormonism - Use of Secondary Sources, Criticism of Mormonism - Sensationalized exaggeration, Criticism of Mormonism - Bait and Switch, Criticism of Mormonism - Secret Teachings, Criticism of Mormonism - Disputed extrapolation, Criticism of Mormonism - Criticism by Former Members, Criticism of Mormonism - Criticisms of Mormonism as contrary to Science, Criticism of Mormonism - Apologetics, Criticism of Mormonism - General Conference and Temple Open House Protests, Criticism of Mormonism - Themes of anti-Mormon protestors, Criticism of Mormonism - Organized criticism to Mormonism, Criticism of Mormonism - Seminars to counter Mormon teachings, Criticism of Mormonism - Intra-Utah Anti Mormonism

Read more here: » Criticism of Mormonism: Encyclopedia II - Criticism of Mormonism - Doctrinal criticism

The field of numerical analysis is divided in different disciplines according to the problem that is to be solved. Numerical analysis - Computing values of functions. One of the simplest problems is the evaluation of a function at a given point. But even evaluating a polynomial is not straightforward: the Horner scheme is often more efficient than the obvious method. Generally, it is important to estimate and control round-off errors arising from the use of floating point arithmetic. Numerical analysis ...

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Numerical analysis, Numerical analysis - General introduction, Numerical analysis - Direct and iterative methods, Numerical analysis - Discretization, Numerical analysis - The generation and propagation of errors, Numerical analysis - Applications, Numerical analysis - Areas of study, Numerical analysis - Computing values of functions, Numerical analysis - Interpolation extrapolation and regression, Numerical analysis - Solving equations and systems of equations, Numerical analysis - Optimization, Numerical analysis - Evaluating integrals, Numerical analysis - Differential equations, Numerical analysis - History, Numerical analysis - Software

Read more here: » Numerical analysis: Encyclopedia II - Numerical analysis - Areas of study

The field of numerical analysis predates the invention of modern computers by many centuries. In fact, many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method. To facilitate computations by hand, large books were produced with formulas and tables of data such as interpolation points and function coefficients. Using these tables, often calculated out to 16 decimal pl ...

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Numerical analysis, Numerical analysis - General introduction, Numerical analysis - Direct and iterative methods, Numerical analysis - Discretization, Numerical analysis - The generation and propagation of errors, Numerical analysis - Applications, Numerical analysis - Areas of study, Numerical analysis - Computing values of functions, Numerical analysis - Interpolation extrapolation and regression, Numerical analysis - Solving equations and systems of equations, Numerical analysis - Optimization, Numerical analysis - Evaluating integrals, Numerical analysis - Differential equations, Numerical analysis - History, Numerical analysis - Software

Read more here: » Numerical analysis: Encyclopedia II - Numerical analysis - History

Nowadays, most algorithms are implemented and run on a computer. The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL and NAG libraries; a free alternative is the GNU Scientific Library. A different approach is taken by the Numerical Recipes library, which emphasizes understanding classic algorithms, as seen by non-specialists. (Some consider this a strengt ...

See also:

Numerical analysis, Numerical analysis - General introduction, Numerical analysis - Direct and iterative methods, Numerical analysis - Discretization, Numerical analysis - The generation and propagation of errors, Numerical analysis - Applications, Numerical analysis - Areas of study, Numerical analysis - Computing values of functions, Numerical analysis - Interpolation extrapolation and regression, Numerical analysis - Solving equations and systems of equations, Numerical analysis - Optimization, Numerical analysis - Evaluating integrals, Numerical analysis - Differential equations, Numerical analysis - History, Numerical analysis - Software

Read more here: » Numerical analysis: Encyclopedia II - Numerical analysis - Software

Nowadays, most algorithms are implemented and run on a computer. The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL and NAG libraries; a free alternative is the GNU Scientific Library. A different approach is taken by the Numerical Recipes library, which emphasizes understanding ...

See also:

Numerical analysis, Numerical analysis - General introduction, Numerical analysis - Direct and iterative methods, Numerical analysis - Discretization, Numerical analysis - The generation and propagation of errors, Numerical analysis - Applications, Numerical analysis - Areas of study, Numerical analysis - Computing values of functions, Numerical analysis - Interpolation extrapolation and regression, Numerical analysis - Solving equations and systems of equations, Numerical analysis - Optimization, Numerical analysis - Evaluating integrals, Numerical analysis - Differential equations, Numerical analysis - History, Numerical analysis - Software

Read more here: » Numerical analysis: Encyclopedia II - Numerical analysis - Software