Quadrature Error Calculation
Contents |
Mathematica Wolfram|Alpha Appliance Enterprise Solutions Corporate Consulting Technical Services Wolfram|Alpha Business Solutions Products for Education Wolfram|Alpha Wolfram|Alpha Pro Problem propagation of error division Generator API Data Drop Mobile Apps Wolfram Cloud App adding errors in quadrature Wolfram|Alpha for Mobile Wolfram|Alpha-Powered Apps Services Paid Project Support Training Summer Programs All Products error propagation formula physics & Services » Technologies Wolfram Language Revolutionary knowledge-based programming language. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Wolfram Science error propagation square root Technology-enabling science of the computational universe. Computable Document Format Computation-powered interactive documents. Wolfram Engine Software engine implementing the Wolfram Language. Wolfram Natural Language Understanding System Knowledge-based broadly deployed natural language. Wolfram Data Framework Semantic framework for real-world data. Wolfram Universal Deployment System Instant deployment across cloud,
Error Propagation Average
desktop, mobile, and more. Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. All Technologies » Solutions Engineering, R&D Aerospace & Defense Chemical Engineering Control Systems Electrical Engineering Image Processing Industrial Engineering Mechanical Engineering Operations Research More... Education All Solutions for Education Web & Software Authoring & Publishing Interface Development Software Engineering Web Development Finance, Statistics & Business Analysis Actuarial Sciences Bioinformatics Data Science Econometrics Financial Risk Management Statistics More... Sciences Astronomy Biology Chemistry More... Trends Internet of Things High-Performance Computing Hackathons All Solutions » Support & Learning Learning Wolfram Language Documentation Fast Introduction for Programmers Training Videos & Screencasts Wolfram Language Introductory Book Virtual Workshops Summer Programs Books Need Help? Support FAQ Wolfram Community Contact Support Premium Support Premier Service Technical Services All Support & Learning » Company About Company Background Wolfram Blog New
a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of
Combination Of Errors In Measurement
differential equations. This article focuses on calculation of definite integrals. The term error propagation chemistry numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as combination of errors cbse class 11 applied to one-dimensional integrals. Some authors refer to numerical integration over more than one dimension as cubature;[1] others take quadrature to include higher-dimensional integration. The basic problem in numerical https://reference.wolfram.com/applications/eda/ExperimentalErrorsAndErrorAnalysis.html integration is to compute an approximate solution to a definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}\!f(x)\,dx} to a given degree of accuracy. If f(x) is a smooth function integrated over a small number of dimensions, and the domain of integration is bounded, there are many methods for approximating the integral to https://en.wikipedia.org/wiki/Numerical_integration the desired precision. Contents 1 History 2 Reasons for numerical integration 3 Methods for one-dimensional integrals 3.1 Quadrature rules based on interpolating functions 3.2 Adaptive algorithms 3.3 Extrapolation methods 3.4 Conservative (a priori) error estimation 3.5 Integrals over infinite intervals 4 Multidimensional integrals 4.1 Monte Carlo 4.2 Sparse grids 4.3 Bayesian Quadrature 5 Connection with differential equations 6 See also 7 References 8 External links 8.1 Free software for numerical integration History[edit] Main article: Quadrature (mathematics) The term "numerical integration" first appears in 1915 in the publication A Course in Interpolation and Numeric Integration for the Mathematical Laboratory by David Gibb.[2] Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the main sources of mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing geometrically a square having the same area (squaring). That is why the process was named quadrature. For example, a quadrature of the circle, Lune of Hippocrates, The Quadrature of the
to get a speed, or adding two lengths to get a total length. Now that we have learned how to determine the error in the directly measured http://www.upscale.utoronto.ca/PVB/Harrison/ErrorAnalysis/Propagation.html quantities we need to learn how these errors propagate to an error in the result. We assume that the two directly measured quantities are X and Y, with errors X and Y respectively. The measurements X and Y must be independent of each other. The fractional error is the value of the error divided by the value of the quantity: X / error propagation X. The fractional error multiplied by 100 is the percentage error. Everything is this section assumes that the error is "small" compared to the value itself, i.e. that the fractional error is much less than one. For many situations, we can find the error in the result Z using three simple rules: Rule 1 If: or: then: In words, this says that the combination of errors error in the result of an addition or subtraction is the square root of the sum of the squares of the errors in the quantities being added or subtracted. This mathematical procedure, also used in Pythagoras' theorem about right triangles, is called quadrature. Rule 2 If: or: then: In this case also the errors are combined in quadrature, but this time it is the fractional errors, i.e. the error in the quantity divided by the value of the quantity, that are combined. Sometimes the fractional error is called the relative error. The above form emphasises the similarity with Rule 1. However, in order to calculate the value of Z you would use the following form: Rule 3 If: then: or equivalently: For the square of a quantity, X2, you might reason that this is just X times X and use Rule 2. This is wrong because Rules 1 and 2 are only for when the two quantities being combined, X and Y, are independent of each other. Here there is only one measurement of one quantity. Question 9.1. Does the first form of Rule 3 look fami
be down. Please try the request again. Your cache administrator is webmaster. Generated Sun, 23 Oct 2016 11:49:21 GMT by s_ac5 (squid/3.5.20)