Error Propagation Rules Wiki
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See also 4 References Software[edit] ASUE This is a powerful web interface powered by webMathematica for evaluating uncertainty symbolically error propagation rules exponents using GUM. Besides, the webpage also allows symbolic uncertainty evaluation
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using ASUE framework (with reference), which is an extension to GUM framework Dempster Shafer with error propagation rules trig Intervals (DSI) Toolbox is a MATLAB toolbox for verified computing under Dempster–Shafer theory. It provides aggregation rules, fast (non-)monotonic function propagation, plots of basic probability
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assignments, verified Fault tree analysis, and much more. EasyGraph is a graphing package that supports error propagation directly into the error bars. Epc is an open source script based tool that calculates the propagation of errors in variables. To quote the text on the Epc web page "This is how to do error propagation done by repeated calculation of the expression using variable-values which are generated using a random number generator whose mean and standard-deviation match the values specified for the variable". Error Calculator Free/libre cross-platform calculator with minimalistic interface. Designed for use in practical courses at natural sciences. Exposes all formulae needed to calculate the results, interoperability with office, support for physical quantities with units. Error Propagation Calculator Free cross-platform calculator (OSX/Windows/Linux) written in Python. Essentially a GUI interface for the python Uncertainties library. Very easy to use and install. ErrorCalc is a scientific calculator app for iPhone or iPad that performs error propagation (Supports Algebraic and RPN modes of entry) FuncDesigner GUMsim is a Monte Carlo simulator and uncertainty estimator for Windows GUM Tree is a design pattern for propagating measurement uncertainty. There is an implementation in R and add-ons for Excel (real and complex numbers). GUM Tree Calculator
1 ( x ) = 1 + x {\displaystyle P_{1}(x)=1+x} (red) at a = 0. The approximation error is the gap
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between the curves, and it increases for x values further from
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0. The approximation error in some data is the discrepancy between an exact value and some approximation to error analysis wiki it. An approximation error can occur because the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is https://en.wikipedia.org/wiki/List_of_uncertainty_propagation_software 4.5cm but since the ruler does not use decimals, you round it to 5cm.) or approximations are used instead of the real data (e.g., 3.14 instead of Ï€). In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm. Contents 1 Formal Definition 1.1 https://en.wikipedia.org/wiki/Approximation_error Generalizations 2 Examples 3 Uses of relative error 4 Instruments 5 See also 6 References 7 External links Formal Definition[edit] One commonly distinguishes between the relative error and the absolute error. Given some value v and its approximation vapprox, the absolute error is ϵ = | v − v approx | , {\displaystyle \epsilon =|v-v_{\text{approx}}|\ ,} where the vertical bars denote the absolute value. If v ≠ 0 , {\displaystyle v\neq 0,} the relative error is η = ϵ | v | = | v − v approx v | = | 1 − v approx v | , {\displaystyle \eta ={\frac {\epsilon }{|v|}}=\left|{\frac {v-v_{\text{approx}}}{v}}\right|=\left|1-{\frac {v_{\text{approx}}}{v}}\right|,} and the percent error is δ = 100 % × η = 100 % × ϵ | v | = 100 % × | v − v approx v | . {\displaystyle \delta =100\%\times \eta =100\%\times {\frac {\epsilon }{|v|}}=100\%\times \left|{\frac {v-v_{\text{approx}}}{v}}\right|.} In words, the absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the
article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2012) (Learn https://en.wikipedia.org/wiki/Delta_rule how and when to remove this template message) This article may be confusing or unclear to readers. Please help us clarify the article; suggestions may be found on the talk page. (September 2012) (Learn how and when to remove this template message) (Learn how and when to remove this template message) In machine learning, the delta rule is a gradient descent learning rule for updating error propagation the weights of the inputs to artificial neurons in a single-layer neural network.[1] It is a special case of the more general backpropagation algorithm. For a neuron j {\displaystyle j\,} with activation function g ( x ) {\displaystyle g(x)\,} , the delta rule for j {\displaystyle j\,} 's i {\displaystyle i\,} th weight w j i {\displaystyle w_{ji}\,} is given by Δ w j error propagation rules i = α ( t j − y j ) g ′ ( h j ) x i {\displaystyle \Delta w_{ji}=\alpha (t_{j}-y_{j})g'(h_{j})x_{i}\,} , where α {\displaystyle \alpha \,} is a small constant called learning rate g ( x ) {\displaystyle g(x)\,} is the neuron's activation function t j {\displaystyle t_{j}\,} is the target output h j {\displaystyle h_{j}\,} is the weighted sum of the neuron's inputs y j {\displaystyle y_{j}\,} is the actual output x i {\displaystyle x_{i}\,} is the i {\displaystyle i\,} th input. It holds that h j = ∑ x i w j i {\displaystyle h_{j}=\sum x_{i}w_{ji}\,} and y j = g ( h j ) {\displaystyle y_{j}=g(h_{j})\,} . The delta rule is commonly stated in simplified form for a neuron with a linear activation function as Δ w j i = α ( t j − y j ) x i {\displaystyle \Delta w_{ji}=\alpha (t_{j}-y_{j})x_{i}\,} While the delta rule is similar to the perceptron's update rule, the derivation is different. The perceptron uses the Heaviside step function as the activation function g ( h ) {\displaystyle g(h)} , and that means that g ′ ( h ) {\dis