Bailey–Borwein–Plouffe formula: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Monkbot
en>Jfmantis
 
Line 1: Line 1:
'''Barnes interpolation''', named after Stanley L. Barnes, is the [[interpolation]] of unstructured data points from a set of measurements of an unknown function in two dimensions into an [[analytic function]] of two variables. An example of a situation where the Barnes scheme is important is in [[weather forecasting]]<ref>{{cite web|url=http://www.bom.gov.au/bmrc/mdev/expt/rainanal/rainanal.shtml|title= Objective Rainfall Analysis System |accessdate=6 May 2009}}</ref><ref>{{cite journal | title=Thunderstorm distribution and frequency in Australia|series=Australian Meteorological Magazine|year=2002|pages=145–154|author=Y.Kuleshov, G. de Hoedt, W.Wright and A.Brewster}}</ref> where measurements are made wherever monitoring stations may be located, the positions of which are constrained by [[topography]]. Such interpolation is essential in data visualisation, e.g. in the construction of [[contour plot]]s or other representations of analytic surfaces.
They are typically a free website that are pre-designed for enabling businesses of every size in marking the presence on the internet and allows them in showcasing the product services and range through images, contents and various other elements. Online available for hiring are most qualified, well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company. Change the site's theme and you have essentially changed the site's personality. Dead links are listed out simply because it will negatively have an influence on the website's search engine rating. The top 4 reasons to use Business Word - Press Themes for a business website are:. <br><br>Luckily, for Word - Press users, WP Touch plugin transforms your site into an IPhone style theme. When you loved this short article and you wish to acquire details relating to [http://go1.in/wordpress_backup_9346237 wordpress dropbox backup] generously pay a visit to our web-page. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. We also help to integrate various plug-ins to expand the functionalities of the web application. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself. <br><br>Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. Note:  at a first glance WP Mobile Pro  themes do not appear to be glamorous or fancy. You've got invested a great cope of time developing and producing up the topic substance. In crux the developer must have a detailed knowledge not only about the marketing tool but also about the ways in which it can be applied profitably. Premium vs Customised Word - Press Themes - Premium themes are a lot like customised themes but without the customised price and without the wait. <br><br>There has been a huge increase in the number of developers releasing free premium Word - Press themes over the years. Russell HR Consulting provides expert knowledge in the practical application of employment law as well as providing employment law training and HR support services. Enterprise, when they plan to hire Word - Press developer resources still PHP, My - SQL and watch with great expertise in codebase. Contact Infertility Clinic Providing One stop Fertility Solutions at:. Make sure you have the latest versions of all your plugins are updated. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. You can select color of your choice, graphics of your favorite, skins, photos, pages, etc. Working with a Word - Press blog and the appropriate cost-free Word - Press theme, you can get a professional internet site up and published in no time at all. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and  full user registration plug-ins.
 
== Introduction ==
Barnes proposed an objective scheme for the interpolation of two dimensional data using a multi-pass scheme.<ref>{{cite journal|first=S. L | last =Barnes |title=A technique for maximizing details in numerical weather-map analysis|journal=Journal of Applied Meteorology|volume=3|issue=4|pages=396&ndash;409|year=1964|url=http://ams.allenpress.com/perlserv/?request=get-abstract&doi=10.1175%2F1520-0450(1964)003%3C0396:ATFMDI%3E2.0.CO%3B2|doi=10.1175/1520-0450(1964)003<0396:ATFMDI>2.0.CO;2|bibcode = 1964JApMe...3..396B }}</ref><ref>{{cite journal | last=Barnes | title=Mesoscale objective analysis using weighted time-series observations|series=NOAA Technical Memorandum|publisher=National Severe Storms laboratory|year=1964|first=S.L}}</ref>  This provided a method to interpolating sea-level pressures across the entire United States of America, producing a [[synoptic chart]] across the country using dispersed monitoring stations. Researchers have subsequently improved the Barnes method to reduce the number of parameters required for calculation of the interpolated result, increasing the objectivity of the method.<ref name="Koch_et_al">{{citation |author=Koch, S. E.,DesJardins, M and Kocin, P|title=An interactive Barnes Objective Map Analysis Scheme for Use with Satelite and Conventional Data|year=1983|journal=Journal of Climate and Applied Meteorology}}</ref>
 
The method constructs a grid of size determined by the distribution of the two dimensional data points. Using this grid, the function values are calculated at each grid point. To do this the method utilises a series of [[Gaussian function]]s, given a [[distance weighting]] in order to determine the relative importance of any given measurement on the determination of the function values. Correction passes are then made to optimise the function values, by accounting for the [[spectral response]] of the interpolated points.
 
== Method ==
Here we describe the method of interpolation used in a multi-pass Barnes interpolation.
 
=== First pass ===
For a given grid point ''i'',&nbsp;''j'' the interpolated function ''g''(''x''<sub>''i''</sub>,&nbsp;''y''<sub>''i''</sub>) is first approximated by the inverse weighting of the data points. To do this as weighting values is assigned to each Gaussian for each grid point, such that
 
: <math>w_{ij} = \exp\left(-\frac{r_m^2}{\kappa}\right), \, </math>
 
where <math>\kappa</math> is a falloff parameter that controls the width of the Gaussian function. This parameter is controlled by the characteristic data spacing, for a fixed Gaussian cutoff radius ''w''<sub>''ij''</sub>&nbsp;=&nbsp;''e''<sup>&minus;1</sup> giving Δ''n'' such that:
 
: <math>\kappa = 5.052\,\frac{2\, \Delta n}{\pi}^2. \, </math>
 
The initial interpolation for the function from the measured values <math>f_k(x,y)</math> then becomes:
 
: <math> g_0(x_i,y_j) = \frac{\displaystyle \sum_k w_{ij} f_k(x,y)}{\displaystyle \sum_k w_{ij}}.</math>
 
=== Second pass ===
The correction for the next pass then utilises the difference between the observed field and the interpolated values at the measurement points to optimise the result:
 
: <math>g_1(x_i,y_j) = g_0(x_i,y_j)  +  \sum( f(x,y) - g_0(x,y)) \exp\left(-\gamma \kappa \frac{\pi}{\lambda}^2\right). \,</math>
 
== Parameter selection ==
Although described as an objective method, there are many parameters which control the interpolated field. The choice of Δ''n'', grid spacing Δ''x'' and <math>\gamma</math> as well influence the final result. Guidelines for the selection of these parameters have been suggested,<ref name="Koch_et_al"/> however the final values used are free to be chosen within these guidelines.
 
The data spacing used in the analysis, Δ''n'' may be chosen either by calculating the true experimental data inter-point spacing, or by the use of a [[complete spatial randomness]] assumption, depending upon the degree of [[Cluster analysis|clustering]] in the observed data. The smoothing parameter <math>\gamma</math> is constrained to be between 0.2 and&nbsp;1.0. For reasons of interpolation integrity, Δ''x'' is argued to be constrained between 0.3 and&nbsp;0.5.
 
== Notes ==
<references/>
 
[[Category:Interpolation]]
[[Category:Spatial data analysis]]

Latest revision as of 00:57, 19 May 2014

They are typically a free website that are pre-designed for enabling businesses of every size in marking the presence on the internet and allows them in showcasing the product services and range through images, contents and various other elements. Online available for hiring are most qualified, well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company. Change the site's theme and you have essentially changed the site's personality. Dead links are listed out simply because it will negatively have an influence on the website's search engine rating. The top 4 reasons to use Business Word - Press Themes for a business website are:.

Luckily, for Word - Press users, WP Touch plugin transforms your site into an IPhone style theme. When you loved this short article and you wish to acquire details relating to wordpress dropbox backup generously pay a visit to our web-page. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. We also help to integrate various plug-ins to expand the functionalities of the web application. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself.

Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. You've got invested a great cope of time developing and producing up the topic substance. In crux the developer must have a detailed knowledge not only about the marketing tool but also about the ways in which it can be applied profitably. Premium vs Customised Word - Press Themes - Premium themes are a lot like customised themes but without the customised price and without the wait.

There has been a huge increase in the number of developers releasing free premium Word - Press themes over the years. Russell HR Consulting provides expert knowledge in the practical application of employment law as well as providing employment law training and HR support services. Enterprise, when they plan to hire Word - Press developer resources still PHP, My - SQL and watch with great expertise in codebase. Contact Infertility Clinic Providing One stop Fertility Solutions at:. Make sure you have the latest versions of all your plugins are updated.

A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. You can select color of your choice, graphics of your favorite, skins, photos, pages, etc. Working with a Word - Press blog and the appropriate cost-free Word - Press theme, you can get a professional internet site up and published in no time at all. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Bailey–Borwein–Plouffe_formula&oldid=264123"