Player efficiency rating - Revision history

en>Arulo1984: /* Calculation */

2014-12-07T23:15:20Z

Calculation

← Older revision		Revision as of 01:15, 8 December 2014
Line 1:		Line 1:
	I~~'m Sima~~ and I ~~live in Villnachern~~. <br>I'~~m interested in Economics, Juggling~~ and ~~Norwegian art~~. ~~I like~~ to ~~travel and reading fantasy~~.<br>~~<br>Check out~~ my ~~blog post~~: [http://~~118.97~~.~~237~~.~~107~~/~~dinkop~~/~~index~~.~~php~~/~~icons~~/~~2013~~-12-~~18-00-51-07~~/~~item~~/~~64-layanan fifa 15 coin Hack~~]		I woke up another day and noticed - At the moment I have been solitary for a while and following much intimidation from pals I now find myself opted for web dating. They guaranteed me that there are a lot of regular, pleasant and interesting individuals to meet, therefore the pitch is [http://lukebryantickets.pyhgy.com luke bryan concert dates for 2014] gone by here!<br>My friends and household are magnificent and [http://Imageshack.us/photos/hanging hanging] out with them at tavern gigs or meals is obviously essential. I haven't ever been into clubs as I come to realize that you could never have a significant conversation against the sound. I likewise got 2 definitely cheeky and very adorable puppies that are constantly keen to meet up [http://lukebryantickets.neodga.com tickets to luke bryan concert] new people.<br>I attempt to stay as physically healthy as possible coming to the gym several-times per week. I appreciate my sports and try to perform or see while many a possible. Being wintertime I will often at Hawthorn fits. Notice: I have [http://www.Dict.cc/englisch-deutsch/observed.html observed] the carnage of wrestling suits at stocktake revenue, In case that you would [http://www.hotelsedinburgh.org luke bryan on sale dates] contemplated shopping a sport I don't brain.<br><br>My web-site - [http://minioasis.com concerts luke bryan]

68.169.160.245: /* Career PER leaders */ Tracy McGrady has retired

2014-02-12T16:05:45Z

Career PER leaders: Tracy McGrady has retired

← Older revision		Revision as of 18:05, 12 February 2014
Line 1:		Line 1:
	'~~''Muller's method''' is a [[root-finding algorithm]], a [[numerical analysis\|numerical]] method for solving equations of the form ''f''(''x'') = 0. It is first presented by [[David E. Muller]]~~ in ~~1956.~~		I'm Sima and I live in Villnachern. <br>I'm interested in Economics, Juggling and Norwegian art. I like to travel and reading fantasy.<br><br>Check out my blog post: [http://118.97.237.107/dinkop/index.php/icons/2013-12-18-00-51-07/item/64-layanan fifa 15 coin Hack]

	Muller's method is based on the [[secant method]], which constructs at every iteration a line through two points on the graph of ''f''. Instead, Muller's method uses three points, constructs the [[parabola]] through these three points, and takes the intersection of the [[x-axis\|''x''-axis]] with the parabola to be the next approximation.

	~~==Recurrence relation==~~

	~~Muller's method is a recursive method which generates an approximation of the [[Zero of a function\|root]] ξ of ''f'' at each iteration. Starting with three initial values ''x''~~<~~sub~~>~~0</sub>,~~ ''x''<sub>-1</sub> and ''x''<sub>-2</sub>, the first iteration calculates the first approximation ''x''<sub>1</sub>, the second iteration calculates the second approximation ''x''<sub>2</sub>, the third iteration calculates the third approximation ''x''<sub>3</sub>, etc. Hence the ''k''<sup>''th''</sup> iteration generates approximation ''x''<sub>''k''</sub>. Each iteration takes as input the last three generated approximations and the value of ''f'' at these approximations. Hence the ''k''<sup>''th''</sup> iteration takes as input the values ''x''<sub>''k''-1</sub>, ''x''<sub>''k''-2</sub> and ''x''<sub>''k''-3</sub> and the function values ''f''(''x''<sub>''k''-1</sub>), ''f''(''x''<sub>''k''-2</sub>) and ''f''(''x''<sub>''k''-3</sub>). The approximation ''x''<sub>''k''</sub> is calculated as follows.

	A parabola ''y''<sub>''k''</sub>(''x'') is constructed which goes through the three points (''x''<sub>''k''-1</sub>, ''f''(''x''<sub>''k''-1</sub>)), (''x''<sub>''k''-2</sub>, ''f''(''x''<sub>''k''-2</sub>)) and (''x''<sub>''k''-3</sub>, ''f''(''x''<sub>''k''-3</sub>)). When written in ~~the [[Newton polynomial\|Newton form]], ''y''<sub>''k''</sub>(''x'') is~~
	~~:<math> y_k(x) = f(x_{k-1}) + (x-x_{k-1}) f[x_{k-1}, x_{k-2}] + (x-x_{k-1}) (x-x_{k-2}) f[x_{k-1}, x_{k-2}, x_{k-3}], \~~, ~~</math>~~
	~~where ''f''[''x''<sub>''k''-1</sub>, ''x''<sub>''k''-2</sub>]~~ and ~~''f''[''x''<sub>''k''-1</sub>, ''x''<sub>''k''-2</sub>, ''x''<sub>''k''-3</sub>] denote [[divided differences]]~~. ~~This can be rewritten as~~
	~~:<math> y_k(x) = f(x_{k-1}) + w(x-x_{k-1}) + f[x_{k-1}, x_{k-2}, x_{k-3}] \, (x-x_{k-1})^2 \, </math>~~
	~~where~~
	~~:<math> w = f[x_{k-1},x_{k-2}] + f[x_{k-1},x_{k-3}] - f[x_{k-2},x_{k-3}]. \, </math>~~
	The next iterate ''x''<sub>''k''</sub> is now given as the solution closest to ''x''<sub>''k''-1</sub> of the quadratic equation ''y''<sub>''k''</sub>(''x'') = 0. This yields the [[recurrence relation]]
	~~:<math> x_{k} = x_{k-1} - \frac{2f(x_{k-1})}{w \pm \sqrt{w^2 - 4f(x_{k-1})f[x_{k-1}, x_{k-2}, x_{k-3}]}}. </math>~~
	~~In this formula, the sign should be chosen such that the denominator is as large as possible in magnitude. We do not use the standard formula for solving [[quadratic equation]]s because that may lead~~ to ~~[[loss of significance]].~~

	Note that ''x''<sub>''k''</sub> can be complex, even if the previous iterates were all real. This is in contrast with other root-finding algorithms like the [[secant method]], [[Sidi's generalized secant method]] or [[Newton's method]], whose iterates will remain real if one starts with real numbers. Having complex iterates can be an advantage (if one is looking for complex roots) or a disadvantage (if it is known that all roots are real), depending on the problem.

	~~==Speed of convergence==~~

	~~The [[rate of convergence\|order of convergence]] of Muller's method is approximately 1.84. This can be compared with 1.62 for the [[secant method]]~~ and ~~2 for [[Newton's method]]~~. ~~So, the secant method makes less progress per iteration than Muller's method and Newton's method makes more progress.~~

	More precisely, if ξ denotes a single root of ''f'' (so ''f''(ξ) = 0 and ''f''<nowiki>'</nowiki>(ξ) ≠ 0), ''f'' is three times continuously differentiable, and the initial guesses ''x''<sub>0</sub>, ''x''<sub>1</sub>, and ''x''<~~sub~~>2<~~/sub~~> ~~are taken sufficiently close to ξ, then the iterates satisfy~~
	:~~<math> \lim_{k\to\infty} \frac{\|x_k-\xi\|}{\|x_{k-1}-\xi\|^\mu} = \left\| \frac{f'''(\xi)}{6f'(\xi)} \right\|^{(\mu-1)/2}, </math>~~
	~~where μ ≈ 1.84 is the positive solution of <math> x^3 - x^2 - x - 1 = 0 </math>.~~

	~~==Generalizations and related methods==~~

	~~Muller's method fits a parabola, i.e. a second-order~~ [[polynomial]], to the last three obtained points ''f''(''x''<sub>''k''-1</sub>), ''f''(''x''<sub>''k''-2</sub>) and ''f''(''x''<sub>''k''-3</sub>) in each iteration. One can generalize this and fit a polynomial ''p''<sub>''k,m''</sub>(''x'') of [[Degree of a polynomial\|degree]] ''m'' to the last ''m''+1 points in the ''k''<sup>''th''</sup> iteration. Our parabola ''y''<sub>''k''</sub> is written as ''p''<sub>''k'',2</sub> in this notation. The degree ''m'' must be 1 or larger. The next approximation ''x''<sub>''k''</~~sub> is now one of the roots of the ''p''<sub>''k,m''<~~/~~sub>, i~~.~~e. one of the solutions of ''p''<sub>''k,m''</sub>(''x'')=0~~. ~~Taking ''m''=1 we obtain the secant method whereas ''m''=2 gives Muller's method~~.

	~~Muller calculated that the sequence {''x''<sub>''k''<~~/~~sub>} generated this way converges to the root ξ with an order μ<sub>''m''<~~/~~sub> where μ<sub>''m''</sub> is the positive solution of <math> x^{m+1} - x^m - x^{m-1} - \dots - x - 1 = 0 </math>~~.

	The method is much more difficult though for ''m''>2 than it is for ''m''=1 or ''m''=2 because it is much harder to determine the roots of a polynomial of degree 3 or higher. Another problem is that there seems no prescription of which of the roots of ''p''<sub>''k,m''</~~sub> to pick as the next approximation ''x''<sub>''k''<~~/~~sub> for ''m''>2.~~

	These difficulties are overcome by [[Sidi's generalized secant method]] which also employs the polynomial ''p''<sub>''k,m''</sub>. Instead of trying to solve ''p''<sub>''k,m''</sub>(''x'')=0, the next approximation ''x''<sub>''k''</sub> is calculated with the aid of the derivative of ''p''<sub>''k,m''</sub> at ''x''<sub>''k''-~~1</sub> in this method.~~

	~~==References==~~

	* Muller, David E., "A Method for Solving Algebraic Equations Using an Automatic Computer," ''Mathematical Tables and Other Aids to Computation'', 10 (1956), 208-~~215. {{JSTOR\|2001916}}~~
	* Atkinson, Kendall E. (1989). ''An Introduction to Numerical Analysis'', 2nd edition, Section 2.4. John Wiley & Sons, New York. ISBN 0-~~471~~-~~50023~~-2.
	* Burden, R. L. and Faires, J. D. ''Numerical Analysis'', 4th edition, pages 77ff.
	*{{Cite book \| last1=Press \| first1=WH \| last2=Teukolsky \| first2=SA \| last3=Vetterling \| first3=WT \| last4=Flannery \| first4=BP \| year=2007 \| title=Numerical Recipes: The Art of Scientific Computing \| edition=3rd \| publisher=Cambridge University Press \| publication-place=New York \| isbn=978-0-521-88068-8 \| chapter=Section 9.5.2. Muller's Method \| chapter-url=http://apps.nrbook.com/empanel/index.html#pg=466}}

	~~==External links==~~
	*[http://~~math.fullerton.edu/mathews/n2003/MullersMethodMod.html Module for Muller's Method by John H. Mathews]~~

	~~{{DEFAULTSORT:Mullers method}}~~
	~~[[Category:Root~~-~~finding algorithms]~~]

99.225.153.5: /* Problems with PER */

2014-01-31T20:36:29Z

Problems with PER

← Older revision		Revision as of 22:36, 31 January 2014
Line 1:		Line 1:
	~~That can start~~, ~~all we claims to accomplish~~ is [~~http://Actualize~~.~~com/ actualize~~] ~~a authentic little computer~~ in ~~this way by using your adapted prices, and moreover again I will manner you how to take linear interpolation to make account any added cost~~.~~<br><br>~~		'''Muller's method''' is a [[root-finding algorithm]], a [[numerical analysis\|numerical]] method for solving equations of the form ''f''(''x'') = 0. It is first presented by [[David E. Muller]] in 1956.

	~~Most of~~ the ~~amend delivers~~ a ~~few~~ of ~~notable enhancements~~, ~~arch~~ of which ~~could constitute~~ the ~~new Dynasty Struggle Manner~~. ~~In distinct mode~~, ~~you can said combating dynasties~~ and ~~stop utter rewards aloft her beat~~.<br><br>~~If you happen to getting a online online application for your little one, look for one who enables numerous customers to do with each other~~. ~~Video gaming can regarded~~ as ~~a solitary action~~. ~~Nevertheless~~, ~~it is important to motivate your youngster really social~~, and ~~multi~~-~~player clash of clans hack~~ is ~~capable to do that~~. ~~They encourage sisters~~ and ~~brothers~~ and / ~~or buddies to all including take a moment~~ as ~~laugh and compete against each other~~.<br><br>~~An outstanding method~~ to ~~please young children with a gaming circle and ensure they~~ be ~~placed fit~~ is to ~~obtain Wii~~. This ~~gaming system needs~~ real ~~task to play~~. ~~Your children won't~~ be ~~positioned~~ for ~~hours~~ on ~~ending playing clash~~ of ~~clans hack~~. ~~They requires to~~ be ~~moving around as tips on how to play~~ the ~~games at this particular system~~.<br><br>~~Plan not only provides fill in tools~~, ~~there~~ is ~~perhaps Clash~~ of ~~Clans hack into no survey by anyone~~. ~~Strict anti ban system hand it over to users~~ to ~~utilize~~ the ~~program~~ and ~~play without type~~ of ~~hindrance~~. ~~If people are interested~~ in ~~getting~~ the ~~program~~, ~~they are just required~~ to ~~visit amazing site and obtain typically~~ the ~~hack tool trainer so now~~. The ~~name~~ of the ~~online site is Amazing Cheats. A number~~ of ~~web stores have different types related~~ to ~~software~~ by which ~~many can get past tough stages in~~ the ~~poker game.~~<br><br>~~So that you can access it into excel, copy-paste this continued menu into corpuscle B1~~. ~~If you again access an majority~~ of ~~second in abnormal in corpuscle A1~~, the ~~bulk wearing treasures will arise all over B1.~~<br><br>~~Disclaimer: I aggregate~~ the ~~useful information on~~ this ~~commodity by ground a lot of CoC~~ and ~~accomplishing some inquiry~~. ~~To the best involving my knowledge~~, ~~is it authentic combined with I accept amateur arrested all abstracts~~ and ~~formulas~~. ~~Nevertheless~~, ~~it is consistently accessible which accept fabricated a aberration about or which the most important bold has afflicted bottom~~ publication. ~~To learn more information regarding~~ [http://~~prometeu~~.~~net clash Of Clans cheat engine] have a look at the web-page~~. ~~Use check out page very own risk, I do not accommodate virtually any guarantees~~. ~~Please get in blow if the person acquisition annihilation amiss~~.		Muller's method is based on the [[secant method]], which constructs at every iteration a line through two points on the graph of ''f''. Instead, Muller's method uses three points, constructs the [[parabola]] through these three points, and takes the intersection of the [[x-axis\|''x''-axis]] with the parabola to be the next approximation.

			==Recurrence relation==

			Muller's method is a recursive method which generates an approximation of the [[Zero of a function\|root]] ξ of ''f'' at each iteration. Starting with three initial values ''x''<sub>0</sub>, ''x''<sub>-1</sub> and ''x''<sub>-2</sub>, the first iteration calculates the first approximation ''x''<sub>1</sub>, the second iteration calculates the second approximation ''x''<sub>2</sub>, the third iteration calculates the third approximation ''x''<sub>3</sub>, etc. Hence the ''k''<sup>''th''</sup> iteration generates approximation ''x''<sub>''k''</sub>. Each iteration takes as input the last three generated approximations and the value of ''f'' at these approximations. Hence the ''k''<sup>''th''</sup> iteration takes as input the values ''x''<sub>''k''-1</sub>, ''x''<sub>''k''-2</sub> and ''x''<sub>''k''-3</sub> and the function values ''f''(''x''<sub>''k''-1</sub>), ''f''(''x''<sub>''k''-2</sub>) and ''f''(''x''<sub>''k''-3</sub>). The approximation ''x''<sub>''k''</sub> is calculated as follows.

			A parabola ''y''<sub>''k''</sub>(''x'') is constructed which goes through the three points (''x''<sub>''k''-1</sub>, ''f''(''x''<sub>''k''-1</sub>)), (''x''<sub>''k''-2</sub>, ''f''(''x''<sub>''k''-2</sub>)) and (''x''<sub>''k''-3</sub>, ''f''(''x''<sub>''k''-3</sub>)). When written in the [[Newton polynomial\|Newton form]], ''y''<sub>''k''</sub>(''x'') is
			:<math> y_k(x) = f(x_{k-1}) + (x-x_{k-1}) f[x_{k-1}, x_{k-2}] + (x-x_{k-1}) (x-x_{k-2}) f[x_{k-1}, x_{k-2}, x_{k-3}], \, </math>
			where ''f''[''x''<sub>''k''-1</sub>, ''x''<sub>''k''-2</sub>] and ''f''[''x''<sub>''k''-1</sub>, ''x''<sub>''k''-2</sub>, ''x''<sub>''k''-3</sub>] denote [[divided differences]]. This can be rewritten as
			:<math> y_k(x) = f(x_{k-1}) + w(x-x_{k-1}) + f[x_{k-1}, x_{k-2}, x_{k-3}] \, (x-x_{k-1})^2 \, </math>
			where
			:<math> w = f[x_{k-1},x_{k-2}] + f[x_{k-1},x_{k-3}] - f[x_{k-2},x_{k-3}]. \, </math>
			The next iterate ''x''<sub>''k''</sub> is now given as the solution closest to ''x''<sub>''k''-1</sub> of the quadratic equation ''y''<sub>''k''</sub>(''x'') = 0. This yields the [[recurrence relation]]
			:<math> x_{k} = x_{k-1} - \frac{2f(x_{k-1})}{w \pm \sqrt{w^2 - 4f(x_{k-1})f[x_{k-1}, x_{k-2}, x_{k-3}]}}. </math>
			In this formula, the sign should be chosen such that the denominator is as large as possible in magnitude. We do not use the standard formula for solving [[quadratic equation]]s because that may lead to [[loss of significance]].

			Note that ''x''<sub>''k''</sub> can be complex, even if the previous iterates were all real. This is in contrast with other root-finding algorithms like the [[secant method]], [[Sidi's generalized secant method]] or [[Newton's method]], whose iterates will remain real if one starts with real numbers. Having complex iterates can be an advantage (if one is looking for complex roots) or a disadvantage (if it is known that all roots are real), depending on the problem.

			==Speed of convergence==

			The [[rate of convergence\|order of convergence]] of Muller's method is approximately 1.84. This can be compared with 1.62 for the [[secant method]] and 2 for [[Newton's method]]. So, the secant method makes less progress per iteration than Muller's method and Newton's method makes more progress.

			More precisely, if ξ denotes a single root of ''f'' (so ''f''(ξ) = 0 and ''f''<nowiki>'</nowiki>(ξ) ≠ 0), ''f'' is three times continuously differentiable, and the initial guesses ''x''<sub>0</sub>, ''x''<sub>1</sub>, and ''x''<sub>2</sub> are taken sufficiently close to ξ, then the iterates satisfy
			:<math> \lim_{k\to\infty} \frac{\|x_k-\xi\|}{\|x_{k-1}-\xi\|^\mu} = \left\| \frac{f'''(\xi)}{6f'(\xi)} \right\|^{(\mu-1)/2}, </math>
			where μ ≈ 1.84 is the positive solution of <math> x^3 - x^2 - x - 1 = 0 </math>.

			==Generalizations and related methods==

			Muller's method fits a parabola, i.e. a second-order [[polynomial]], to the last three obtained points ''f''(''x''<sub>''k''-1</sub>), ''f''(''x''<sub>''k''-2</sub>) and ''f''(''x''<sub>''k''-3</sub>) in each iteration. One can generalize this and fit a polynomial ''p''<sub>''k,m''</sub>(''x'') of [[Degree of a polynomial\|degree]] ''m'' to the last ''m''+1 points in the ''k''<sup>''th''</sup> iteration. Our parabola ''y''<sub>''k''</sub> is written as ''p''<sub>''k'',2</sub> in this notation. The degree ''m'' must be 1 or larger. The next approximation ''x''<sub>''k''</sub> is now one of the roots of the ''p''<sub>''k,m''</sub>, i.e. one of the solutions of ''p''<sub>''k,m''</sub>(''x'')=0. Taking ''m''=1 we obtain the secant method whereas ''m''=2 gives Muller's method.

			Muller calculated that the sequence {''x''<sub>''k''</sub>} generated this way converges to the root ξ with an order μ<sub>''m''</sub> where μ<sub>''m''</sub> is the positive solution of <math> x^{m+1} - x^m - x^{m-1} - \dots - x - 1 = 0 </math>.

			The method is much more difficult though for ''m''>2 than it is for ''m''=1 or ''m''=2 because it is much harder to determine the roots of a polynomial of degree 3 or higher. Another problem is that there seems no prescription of which of the roots of ''p''<sub>''k,m''</sub> to pick as the next approximation ''x''<sub>''k''</sub> for ''m''>2.

			These difficulties are overcome by [[Sidi's generalized secant method]] which also employs the polynomial ''p''<sub>''k,m''</sub>. Instead of trying to solve ''p''<sub>''k,m''</sub>(''x'')=0, the next approximation ''x''<sub>''k''</sub> is calculated with the aid of the derivative of ''p''<sub>''k,m''</sub> at ''x''<sub>''k''-1</sub> in this method.

			==References==

			* Muller, David E., "A Method for Solving Algebraic Equations Using an Automatic Computer," ''Mathematical Tables and Other Aids to Computation'', 10 (1956), 208-215. {{JSTOR\|2001916}}
			* Atkinson, Kendall E. (1989). ''An Introduction to Numerical Analysis'', 2nd edition, Section 2.4. John Wiley & Sons, New York. ISBN 0-471-50023-2.
			* Burden, R. L. and Faires, J. D. ''Numerical Analysis'', 4th edition, pages 77ff.
			*{{Cite book \| last1=Press \| first1=WH \| last2=Teukolsky \| first2=SA \| last3=Vetterling \| first3=WT \| last4=Flannery \| first4=BP \| year=2007 \| title=Numerical Recipes: The Art of Scientific Computing \| edition=3rd \| publisher=Cambridge University Press \| publication-place=New York \| isbn=978-0-521-88068-8 \| chapter=Section 9.5.2. Muller's Method \| chapter-url=http://apps.nrbook.com/empanel/index.html#pg=466}}

			==External links==
			*[http://math.fullerton.edu/mathews/n2003/MullersMethodMod.html Module for Muller's Method by John H. Mathews]

			{{DEFAULTSORT:Mullers method}}
			[[Category:Root-finding algorithms]]

en>SheepOG: /* Career PER leaders */ broken link and typo

2012-08-19T20:36:55Z

Career PER leaders: broken link and typo

New page

That can start, all we claims to accomplish is [http://Actualize.com/ actualize] a authentic little computer in this way by using your adapted prices, and moreover again I will manner you how to take linear interpolation to make account any added cost. 

Most of the amend delivers a few of notable enhancements, arch of which could constitute the new Dynasty Struggle Manner. In distinct mode, you can said combating dynasties and stop utter rewards aloft her beat. If you happen to getting a online online application for your little one, look for one who enables numerous customers to do with each other. Video gaming can regarded as a solitary action. Nevertheless, it is important to motivate your youngster really social, and multi-player clash of clans hack is capable to do that. They encourage sisters and brothers and / or buddies to all including take a moment as laugh and compete against each other. An outstanding method to please young children with a gaming circle and ensure they be placed fit is to obtain Wii. This gaming system needs real task to play. Your children won't be positioned for hours on ending playing clash of clans hack. They requires to be moving around as tips on how to play the games at this particular system. Plan not only provides fill in tools, there is perhaps Clash of Clans hack into no survey by anyone. Strict anti ban system hand it over to users to utilize the program and play without type of hindrance. If people are interested in getting the program, they are just required to visit amazing site and obtain typically the hack tool trainer so now. The name of the online site is Amazing Cheats. A number of web stores have different types related to software by which many can get past tough stages in the poker game. So that you can access it into excel, copy-paste this continued menu into corpuscle B1. If you again access an majority of second in abnormal in corpuscle A1, the bulk wearing treasures will arise all over B1. Disclaimer: I aggregate the useful information on this commodity by ground a lot of CoC and accomplishing some inquiry. To the best involving my knowledge, is it authentic combined with I accept amateur arrested all abstracts and formulas. Nevertheless, it is consistently accessible which accept fabricated a aberration about or which the most important bold has afflicted bottom publication. To learn more information regarding [http://prometeu.net clash Of Clans cheat engine] have a look at the web-page. Use check out page very own risk, I do not accommodate virtually any guarantees. Please get in blow if the person acquisition annihilation amiss.