Propagation Of Error Numerical Methods
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numbers to powers, propagation error etc. can be determined with specific analytical formulas. However,
Error Propagation Example
the analysis of the propagation of errors through a model is frequently most easily accomplished numerically. Analytical Methods Formulas for functions of one variable Formulas for functions of two variables « Previous Page Next Page » Quantitative Skills Issues and Discussion Teaching Methods Back of the Envelope Calculations Mathematical and Statistical Models Measurement and Uncertainty Metacognition Models Teaching Quantitative Literacy Teaching Quantitative Reasoning with the News Teaching with Data Teaching with Data Simulations Teaching with Equations Teaching with SSAC Understanding Uncertainty Appropriate Representation of Numbers Significant Figures Rounding Numbers Propagation of Error Precision and Accuracy Measurement Error Teaching Resources Settings Tools and Datasets Community Last Modified: June 21, 2012 | Printing | Shortcut: http://serc.carleton.edu/37886 | Privacy | Terms of Use | Report a Problem/Feedback
general: Multiplication and division are “safe” operations Addition and subtraction are dangerous, because when numbers of different magnitudes are involved, digits of the smaller-magnitude number are lost. This loss of digits can be inevitable and benign (when the lost digits also insignificant for the final result) or catastrophic (when the loss is magnified and distorts http://serc.carleton.edu/quantskills/teaching_methods/und_uncertainty/errpropagation.html the result strongly). The more calculations are done (especially when they form an iterative algorithm) the more important it is to consider this kind of problem. A method of calculation can be stable (meaning that it tends to reduce rounding errors) or unstable (meaning that http://floating-point-gui.de/errors/propagation/ rounding errors are magnified). Very often, there are both stable and unstable solutions for a problem. There is an entire sub-field of mathematics (in numerical analysis) devoted to studying the numerical stability of algorithms. For doing complex calculations involving floating-point numbers, it is absolutely necessary to have some understanding of this discipline. The article What Every Computer Scientist Should Know About Floating-Point Arithmetic gives a detailed introduction, and served as an inspiration for creating this website, mainly due to being a bit too detailed and intimidating to programmers without a scientific background. © Published at floating-point-gui.de under the Creative Commons Attribution License (BY) The Floating-Point Guide Home Basic Answers References xkcd Number Formats Binary Fractions Floating-Point Exact Types On Using Integers Errors Rounding Comparison Propagation Languagecheat sheets C# Java JavaScript Perl PHP Python Ruby SQL
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