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Error Analysis (mathematics)
In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such as numerical analysis and statistics. Error analysis in numerical modeling In numerical simulation or modeling of real systems, error analysis is concerned with the changes in the output of the model as the parameters to the model vary about a mean. For instance, in a system modeled as a function of two variables z \,=\, f(x,y). Error analysis deals with the propagation of the numerical errors in x and y (around mean values \bar and \bar) to error in z (around a mean \bar). In numerical analysis, error analysis comprises both forward error analysis and backward error analysis. Forward error analysis Forward error analysis involves the analysis of a function z' = f'(a_0,\,a_1,\,\dots,\,a_n) which is an approximation (usually a finite polynomial) to a function z \,=\, f(a_0,a_1,\do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error
An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistics, "error" refers to the difference between the value which has been computed and the correct value. An error could result in failure or in a deviation from the intended performance or behavior. Human behavior One reference differentiates between "error" and "mistake" as follows: In human behavior the norms or expectations for behavior or its consequences can be derived from the intention of the actor or from the expectations of other individuals or from a social grouping or from social norms. (See deviance.) Gaffes and faux pas can be labels for certain instances of this kind of error. More serious departures from social norms carry labels such as misbehavior and labels from the legal system, such as misdemeanor and crime. Departures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. The method is applied mostly in chemical physics, materials science, and biophysics. Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods. However, long MD simulations are mathematically ill-conditioned, generating cumulative errors in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Validated Numerics
Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification (german: Zuverlässiges Rechnen) is numerics including mathematically strict error (rounding error, truncation error, discretization error) evaluation, and it is one field of numerical analysis. For computation, interval arithmetic is used, and all results are represented by intervals. Validated numerics were used by Warwick Tucker in order to solve the 14th of Smale's problems, and today it is recognized as a powerful tool for the study of dynamical systems. Importance Computation without verification may cause unfortunate results. Below are some examples. Rump's example In the 1980s, Rump made an example. He made a complicated function and tried to obtain its value. Single precision, double precision, extended precision results seemed to be correct, but its plus-minus sign was different from the true value. Phantom solution Breuer–Plum–McKenna used the spectrum m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propagation Of Uncertainty
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function. The uncertainty ''u'' can be expressed in a number of ways. It may be defined by the absolute error . Uncertainties can also be defined by the relative error , which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, , which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval . If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Errors And Residuals In Statistics
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the ''estimated'' value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances. Introduction Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Bar
Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a particular confidence interval (e.g., a 95% interval). These quantities are not the same and so the measure selected should be stated explicitly in the graph or supporting text. Error bars can be used to compare visually two quantities if various other conditions hold. This can determine whether differences are statistically significant. Error bars can also suggest goodness of fit of a given function, i.e., how well the function describes the data. Scientific papers in the experimental sciences are expected to include error bars on all graphs, though the practice differs somewhat between sciences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Analysis (linguistics)
In linguistics, according to J. Richard et al., (2002), an error is the use of a word, speech act or grammatical items in such a way that it seems imperfect and significant of an incomplete learning (184). It is considered by Norrish (1983, p. 7) as a systematic deviation which happens when a learner has not learnt something, and consistently gets it wrong. However, the attempts made to put the error into context have always gone hand in hand with either anguage learning and second-language acquisitionprocesse, Hendrickson (1987:357) mentioned that errors are ‘signals’ that indicate an actual learning process taking place and that the learner has not yet mastered or shown a well-structured competencein the target language. All the definitions seeme to stress either on the systematic deviations triggered in the language learning process, or its indications of the actual situation of the language learner themselves, which will later help monitoring, be it an applied linguis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Averaging
Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 the Block '' * WFNZ-FM, a radio station licensed to Harrisburg, North Carolina, United States, branded as ''92.7 The Block'' * Blocked (''The Flash''), an episode of the television series ''The Flash'' Music * Block Entertainment, a record label * Blocks Recording Club, a record label * Woodblock (instrument), a small piece of slit drum made from one piece of wood and used as a percussion instrument * "Blocks", by C418 from '' Minecraft - Volume Beta'', 2013 Toys * Toy block, one of a set of wooden or plastic pieces, of various shapes * Unit block, a type of standardized wooden toy block for children Video game * Blocked (video game), a puzzle game for the iPhone and iPod Touch Building and construction * Breeze block, cinder block o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Bar
Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a particular confidence interval (e.g., a 95% interval). These quantities are not the same and so the measure selected should be stated explicitly in the graph or supporting text. Error bars can be used to compare visually two quantities if various other conditions hold. This can determine whether differences are statistically significant. Error bars can also suggest goodness of fit of a given function, i.e., how well the function describes the data. Scientific papers in the experimental sciences are expected to include error bars on all graphs, though the practice differs somewhat between sciences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autocorrelation Function
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Positioning System
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite systems (GNSS) that provides geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. It does not require the user to transmit any data, and operates independently of any telephonic or Internet reception, though these technologies can enhance the usefulness of the GPS positioning information. It provides critical positioning capabilities to military, civil, and commercial users around the world. Although the United States government created, controls and maintains the GPS system, it is freely accessible to anyone with a GPS receiver. The GPS project was started by the U.S. Department of Defense in 1973. The first prototype spacecraft was lau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
