Backward Error Analysis Definition
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issue is particularly prominent in applied areas such as numerical analysis and statistics. Contents 1 error analysis definition chemistry Error analysis in numerical modeling 1.1 Forward error analysis 1.2 Backward error analysis definition physics error analysis 2 Applications 2.1 Global positioning system 2.2 Molecular dynamics simulation 2.3 Scientific data verification error analysis definition linguistics 3 See also 4 References 5 External links Error analysis in numerical modeling[edit] In numerical simulation or modeling of real systems, error analysis is concerned with
Backward Error Correction
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 ) {\displaystyle \scriptstyle z\,=\,f(x,y)} . Error analysis deals with the propagation of the numerical errors definition miscue analysis in x {\displaystyle \scriptstyle x} and y {\displaystyle \scriptstyle y} (around mean values x ¯ {\displaystyle \scriptstyle {\bar {x}}} and y ¯ {\displaystyle \scriptstyle {\bar {y}}} ) to error in z {\displaystyle \scriptstyle z} (around a mean z ¯ {\displaystyle \scriptstyle {\bar {z}}} ).[1] In numerical analysis, error analysis comprises both forward error analysis and backward error analysis. Forward error analysis[edit] Forward error analysis involves the analysis of a function z ′ = f ′ ( a 0 , a 1 , … , a n ) {\displaystyle \scriptstyle 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 , … , a n ) {\displaystyle \scriptstyle z\,=\,f(a_{0},a_{1},\dots ,a_{n})} to determine the bounds on the error in the approximation; i.e., to find ϵ {\displaystyle \scriptstyle \epsilon } such that 0 ≤ | z − z ′ | ≤ ϵ {\displaystyle \scriptstyle 0\,\leq \,|z-z'|\,\leq \,\eps
the forward https://en.wikipedia.org/wiki/Error_analysis_(mathematics) and backward error analysis. Backward error propagation: How much error in input would be required to explain http://www.physics.arizona.edu/~restrepo/475A/Notes/sourcea-/node13.html all output error? Assumes that approximate solution to problem is good IF IT IS THE exact solution to a ``nearby'' problem. Example Want to approximate . We evaluate its accuracy at . Backward Error: 1) Find such that The following are different and cannot be compared: Juan Restrepo 2003-04-12
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