Tfzero - Revision history

Elias at 12:07, 10 January 2012

2012-01-10T12:07:54Z

← Older revision		Revision as of 07:07, 10 January 2012
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	==Calling Syntax==		==Calling Syntax==

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	[xLow, xUpp, ExitFlag] = Tfzero(x_L, x_U, Prob, x_0, RelErr, AbsErr)		[xLow, xUpp, ExitFlag] = Tfzero(x_L, x_U, Prob, x_0, RelErr, AbsErr)
	</~~syntaxhighlight~~>		</source>

	==Description of Inputs==		==Description of Inputs==

Elias: /* Outputs */

2011-07-21T13:21:02Z

Outputs

← Older revision		Revision as of 08:21, 21 July 2011
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	{\| class="wikitable"		{\| class="wikitable"
	\|''Variable''\|\|Description		!''Variable''\|\|Description
	\|-		\|-
	\|''xLow''\|\|Lower limit on the zero x to f(x).		\|''xLow''\|\|Lower limit on the zero x to f(x).

Elias: /* Description of Inputs */

2011-07-21T13:20:52Z

Description of Inputs

← Older revision		Revision as of 08:20, 21 July 2011
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	{\| class="wikitable"		{\| class="wikitable"
	\|''Variable''\|\|Description		!''Variable''\|\|Description
	\|-		\|-
	\|''x_L''\|\|Lower limit on the zero x to f(x).		\|''x_L''\|\|Lower limit on the zero x to f(x).

Elias at 13:18, 21 July 2011

2011-07-21T13:18:15Z

← Older revision		Revision as of 08:18, 21 July 2011
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	[[Category:Solvers]]		[[Category:Solvers]]
	~~{{cleanup\|Clean this article.}}~~

	==Purpose==		==Purpose==

	~~Tfzero, TOMLAB fzero routine.~~		Find a zero for <math>f(x)</math> in the interval <math>[x_L, x_U]</math>. Tfzero searches for a zero of a function <math>f(x)</math> between the given scalar values <math>x_L</math> and <math>x_U</math> until the width of the interval (xLow, xUpp) has collapsed to within a tolerance specified by the stopping criterion, <math>abs(xLow-xUpp) <= 2.(RelErrabs(xLow)+AbsErr)</math>. The method used is an efficient combination of bisection and the secant rule and is due to T. J. Dekker.

	~~Tfzero, TOMLAB fzero routine.\\ \\~~Find a zero for <math>f(x)</math> in the interval <math>[x_L, x_U]</math>. Tfzero searches for a zero of a function <math>f(x)</math> between the given scalar values <math>x_L</math> and <math>x_U</math> until the width of the interval (xLow, xUpp) has collapsed to within a tolerance specified by the stopping criterion, <math>abs(xLow-xUpp) <= 2.(RelErrabs(xLow)+AbsErr)</math>. The method used is an efficient combination of bisection and the secant rule and is due to T. J. Dekker.

	==Calling Syntax==		==Calling Syntax==

	[xLow, xUpp, ExitFlag] = Tfzero(~~x L~~, ~~x U~~, Prob, ~~x 0~~, RelErr, AbsErr)		<syntaxhighlight lang="matlab">
			[xLow, xUpp, ExitFlag] = Tfzero(x_L, x_U, Prob, x_0, RelErr, AbsErr)
			</syntaxhighlight>

	===Description of Inputs===		==Description of Inputs==

	{\|		{\| class="wikitable"
	\|''Variable''\|\|Description		\|''Variable''\|\|Description
	\|-		\|-
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	\|}		\|}

	==~~=Description of~~ Outputs===		==Outputs==

	{\|		{\| class="wikitable"
	\|''Variable''\|\|Description		\|''Variable''\|\|Description
	\|-		\|-
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	\|-		\|-
	\|''xUpp''\|\|Upper limit on the zero x to f(x).		\|''xUpp''\|\|Upper limit on the zero x to f(x).
	\|-		\|-valign="top"
	\|''ExitFlag''\|\|Status flag 1,2,3,4,5.		\|''ExitFlag''\|\|Status flag 1,2,3,4,5.
	\|-
	~~\|\|\|~~1: xLow is within the requested tolerance of a zero. The interval (xLow, xUpp) collapsed to the requested tolerance, the function changes sign in (xLow, xUpp), and f(x) decreased in magnitude as (xLow, xUpp) collapsed.		1: xLow is within the requested tolerance of a zero. The interval (xLow, xUpp) collapsed to the requested tolerance, the function changes sign in (xLow, xUpp), and f(x) decreased in magnitude as (xLow, xUpp) collapsed.
	\|-
	~~\|\|\|~~2: f(xLow) = 0. However, the interval (xLow, xUpp) may not have collapsed to the requested tolerance.		2: f(xLow) = 0. However, the interval (xLow, xUpp) may not have collapsed to the requested tolerance.
	\|-
	~~\|\|\|~~3: xLow may be near a singular point of f(x). The interval (xLow, xUpp) collapsed to the requested tolerance and the function changes sign in (xLow, xUpp), but f(x) increased in magnitude as (xLow, xUpp) collapsed, i.e. ''abs''(''f ''(''xLow'')) ''> max''(''abs''(''f ''(''xLow - ~~I N~~ ''))'', abs''(''f ''(''~~xU pp~~ - ~~I N~~ ''))).		3: xLow may be near a singular point of f(x). The interval (xLow, xUpp) collapsed to the requested tolerance and the function changes sign in (xLow, xUpp), but f(x) increased in magnitude as (xLow, xUpp) collapsed, i.e. ''abs''(''f''(''xLow'')) ''> max''(''abs''(''f''(''xLow - IN ''))'', abs''(''f''(''xUpp - IN ''))).
	\|-
	~~\|\|\|~~4: No change in sign of f(x) was found although the interval (xLow, xUpp) collapsed to the requested tolerance. The user must examine this case and decide whether xLow is near a local minimum of f(x), or xLow is near a zero of even multiplicity, or neither of these.		4: No change in sign of f(x) was found although the interval (xLow, xUpp) collapsed to the requested tolerance. The user must examine this case and decide whether xLow is near a local minimum of f(x), or xLow is near a zero of even multiplicity, or neither of these.
	\|-
	~~\|\|\|~~5: Too many (> 500) function evaluations used.		5: Too many (> 500) function evaluations used.
	\|}		\|}

Elias at 12:24, 11 July 2011

2011-07-11T12:24:06Z

← Older revision		Revision as of 07:24, 11 July 2011
Line 1:		Line 1:
			[[Category:Solvers]]
			{{cleanup\|Clean this article.}}

	==Purpose==		==Purpose==

Elias: Created page with "==Purpose== Tfzero, TOMLAB fzero routine. Tfzero, TOMLAB fzero routine.\\ \\Find a zero for $f(x)$ in the interval $[x_L, x_U]$ . Tfzero searches for a ze..."

2011-07-11T12:04:52Z

Created page with "==Purpose== Tfzero, TOMLAB fzero routine. Tfzero, TOMLAB fzero routine.\\ \\Find a zero for <math>f(x)</math> in the interval <math>[x_L, x_U]</math>. Tfzero searches for a ze..."

New page

==Purpose==

Tfzero, TOMLAB fzero routine.

Tfzero, TOMLAB fzero routine.\\ \\Find a zero for <math>f(x)</math> in the interval <math>[x_L, x_U]</math>. Tfzero searches for a zero of a function <math>f(x)</math> between the given scalar values <math>x_L</math> and <math>x_U</math> until the width of the interval (xLow, xUpp) has collapsed to within a tolerance specified by the stopping criterion, <math>abs(xLow-xUpp) <= 2.*(RelErr*abs(xLow)+AbsErr)</math>. The method used is an efficient combination of bisection and the secant rule and is due to T. J. Dekker.

==Calling Syntax==

[xLow, xUpp, ExitFlag] = Tfzero(x L, x U, Prob, x 0, RelErr, AbsErr)

===Description of Inputs===

{|
|''Variable''||Description
|-
|''x_L''||Lower limit on the zero x to f(x).
|-
|''x_U''||Upper limit on the zero x to f(x).
|-valign="top"
|''Prob''||Structure, sent to Matlab routine ZeroFunc. The function name should be set in Prob.FUNCS.f0. Only the function will be used, not the gradient.
|-
|''x_0''||An initial guess on the zero to f(x). If empty, x 0 is set as the middle point in [x_L, x_U].
|-
|''RelErr''||Relative error tolerance, default 1E-7.
|-
|''AbsErr''||Absolute error tolerance, default 1E-14.
|}

===Description of Outputs===

{|
|''Variable''||Description
|-
|''xLow''||Lower limit on the zero x to f(x).
|-
|''xUpp''||Upper limit on the zero x to f(x).
|-
|''ExitFlag''||Status flag 1,2,3,4,5.
|-
|||1: xLow is within the requested tolerance of a zero. The interval (xLow, xUpp) collapsed to the requested tolerance, the function changes sign in (xLow, xUpp), and f(x) decreased in magnitude as (xLow, xUpp) collapsed.
|-
|||2: f(xLow) = 0. However, the interval (xLow, xUpp) may not have collapsed to the requested tolerance.
|-
|||3: xLow may be near a singular point of f(x). The interval (xLow, xUpp) collapsed to the requested tolerance and the function changes sign in (xLow, xUpp), but f(x) increased in magnitude as (xLow, xUpp) collapsed, i.e. ''abs''(''f ''(''xLow'')) ''> max''(''abs''(''f ''(''xLow - I N ''))'', abs''(''f ''(''xU pp - I N ''))).
|-
|||4: No change in sign of f(x) was found although the interval (xLow, xUpp) collapsed to the requested tolerance. The user must examine this case and decide whether xLow is near a local minimum of f(x), or xLow is near a zero of even multiplicity, or neither of these.
|-
|||5: Too many (> 500) function evaluations used.
|}