ITERATE - Revision history

Jrheinlaender at 19:38, 26 September 2024

2024-09-26T19:38:01Z

← Older revision		Revision as of 19:38, 26 September 2024
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	<code>EXDEF ITERATE(x = cos(x), ~~100~~, 0.01, 100)</code> will start iterating with <code>x=~~100~~</code>. The next value of <code>x</code> will be <code>~~sqrt~~(~~100~~)</code>. The result of the iteration will be approximately 0.74, since that is the solution of the equation <code>cos(x) - x = 0</code>		<code>EXDEF ITERATE(x = cos(x), 0.5, 0.01, 100)</code> will start iterating with <code>x=0.5</code>. The next value of <code>x</code> will be <code>cos(0.5)</code>. The result of the iteration will be approximately 0.74, since that is the solution of the equation <code>cos(x) - x = 0</code>

	<code>EQDEF (stack{x#y}) = ITERATE(x = cos(y);y = cos(x), 1;1, 0.01;0.01, 100)</code> boils down to finding values of <code>x</code> and <code>y</code> where <code>x - cos y = 0</code> and <code>y - cos(x) = 0</code>, that is <code>x/y = cos y/cos x</code>. The resulting value e.g. for <code>x</code> can be accessed with <code>VAL(x)</code>.		<code>EQDEF (stack{x#y}) = ITERATE(x = cos(y);y = cos(x), 1;1, 0.01;0.01, 100)</code> boils down to finding values of <code>x</code> and <code>y</code> where <code>x - cos y = 0</code> and <code>y - cos(x) = 0</code>, that is <code>x/y = cos y/cos x</code>. The resulting value e.g. for <code>x</code> can be accessed with <code>VAL(x)</code>.

Jrheinlaender at 16:31, 1 November 2017

2017-11-01T16:31:07Z

← Older revision		Revision as of 16:31, 1 November 2017
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	It is highly recommended to set the maximum number of iterations to a very low value when testing new expressions. If for some reason the expression on the right-hand side does not evaluate to a numeric value, then <code>ITERATE</code> can create huge symbolic expressions!		It is highly recommended to set the maximum number of iterations to a very low value when testing new expressions. If for some reason the expression on the right-hand side does not evaluate to a numeric value, then <code>ITERATE</code> can create huge symbolic expressions!

	The second form of <code>ITERATE</code> iterates a list of equations that may depend on one another. The result is a vector. ~~ITERATE sets the values of~~ the variables ~~on the left-hand side of the equations~~, ~~so they can be accessed later with~~ a ~~[[VAL]] statement~~.		The second form of <code>ITERATE</code> iterates a list of equations that may depend on one another. The result is a vector. If you want to assign this result to the corresponding variables, assign it to a column vector.
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	<code>EXDEF ITERATE(x = cos(x), 100, 0.01, 100)</code> will start iterating with <code>x=100</code>. The next value of <code>x</code> will be <code>sqrt(100)</code>. The result of the iteration will be approximately 0.74, since that is the solution of the equation <code>cos(x) - x = 0</code>		<code>EXDEF ITERATE(x = cos(x), 100, 0.01, 100)</code> will start iterating with <code>x=100</code>. The next value of <code>x</code> will be <code>sqrt(100)</code>. The result of the iteration will be approximately 0.74, since that is the solution of the equation <code>cos(x) - x = 0</code>

	<code>EQDEF v = ITERATE(x = cos(y);y = cos(x), 1;1, 0.01;0.01, 100)</code> boils down to finding values of <code>x</code> and <code>y</code> where <code>x - cos y = 0</code> and <code>y - cos(x) = 0</code>, that is <code>x/y = cos y/cos x</code>. The resulting value e.g. for <code>x</code> can be accessed ~~as <code>VAL(v[1])</code> or directly~~ with <code>VAL(x)</code>.		<code>EQDEF (stack{x#y}) = ITERATE(x = cos(y);y = cos(x), 1;1, 0.01;0.01, 100)</code> boils down to finding values of <code>x</code> and <code>y</code> where <code>x - cos y = 0</code> and <code>y - cos(x) = 0</code>, that is <code>x/y = cos y/cos x</code>. The resulting value e.g. for <code>x</code> can be accessed with <code>VAL(x)</code>.
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	[[Category:Manipulation]]		[[Category:Manipulation]]

Jrheinlaender at 14:27, 2 July 2017

2017-07-02T14:27:32Z

← Older revision		Revision as of 14:27, 2 July 2017
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	Iterate an equation of the form <code>[[~~variable~~]] = [[expression]]</code> until it converges, that is, the difference between two consecutive values of the variable is less than the limit given as the third parameter. In every iteration step, the value of the variable found in the previous step is inserted into the expression on the right-hand side.		Iterate an equation of the form <code>[[symbol]] = [[expression]]</code> until it converges, that is, the difference between two consecutive values of the variable is less than the limit given as the third parameter. In every iteration step, the value of the variable found in the previous step is inserted into the expression on the right-hand side.

	The last parameter gives the maximum number of iterations, in case there is no convergence.		The last parameter gives the maximum number of iterations, in case there is no convergence.

Jrheinlaender at 19:22, 27 June 2017

2017-06-27T19:22:45Z

← Older revision		Revision as of 19:22, 27 June 2017
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	<code>EQDEF v = ITERATE(x = cos(y);y = cos(x), 1;1, 0.01;0.01, 100)</code> boils down to finding values of <code>x</code> and <code>y</code> where <code>x - cos y = 0</code> and <code>y - cos(x) = 0</code>, that is <code>x/y = cos y/cos x</code>. The resulting value e.g. for <code>x</code> can be accessed as <code>VAL(v[1])</code> or directly with <code>VAL(x)</code>.		<code>EQDEF v = ITERATE(x = cos(y);y = cos(x), 1;1, 0.01;0.01, 100)</code> boils down to finding values of <code>x</code> and <code>y</code> where <code>x - cos y = 0</code> and <code>y - cos(x) = 0</code>, that is <code>x/y = cos y/cos x</code>. The resulting value e.g. for <code>x</code> can be accessed as <code>VAL(v[1])</code> or directly with <code>VAL(x)</code>.
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	}}		}}
	[[Category:Manipulation]]		[[Category:Manipulation]]

Jrheinlaender: Created page with "{{Keyword | 1= `ITERATE ( equation, expression, expression, integer )` `ITERATE (equation list, expression list, expression list, inte..."`


2017-04-15T09:26:06Z
Created page with "{{Keyword | 1= <code>ITERATE ( equation, expression, expression, integer )</code>  <code>ITERATE (equation list, expression list, expression list, inte..."
New page
{{Keyword

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1=

<code>ITERATE ( [[equation]], [[expression]], [[expression]], integer )</code>



<code>ITERATE ([[equation list]], [[expression list]], [[expression list]], integer )</code>

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Iterate an equation of the form <code>[[variable]] = [[expression]]</code> until it converges, that is, the difference between two consecutive values of the variable is less than the limit given as the third parameter. In every iteration step, the value of the variable found in the previous step is inserted into the expression on the right-hand side.



The last parameter gives the maximum number of iterations, in case there is no convergence. 



It is highly recommended to set the maximum number of iterations to a very low value when testing new expressions. If for some reason the expression on the right-hand side does not evaluate to a numeric value, then <code>ITERATE</code> can create huge symbolic expressions!



The second form of <code>ITERATE</code> iterates a list of equations that may depend on one another. The result is a vector. ITERATE sets the values of the variables on the left-hand side of the equations, so they can be accessed later with a [[VAL]] statement.

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3=

<code>EXDEF ITERATE(x = cos(x), 100, 0.01, 100)</code> will start iterating with <code>x=100</code>. The next value of <code>x</code> will be <code>sqrt(100)</code>.  The result of the iteration will be approximately 0.74, since that is the solution of the equation <code>cos(x) - x = 0</code>



<code>EQDEF v = ITERATE(x = cos(y);y = cos(x), 1;1, 0.01;0.01, 100)</code> boils down to finding values of <code>x</code> and <code>y</code> where <code>x - cos y = 0</code> and <code>y - cos(x) = 0</code>, that is <code>x/y = cos y/cos x</code>. The resulting value e.g. for <code>x</code> can be accessed as <code>VAL(v[1])</code> or directly with <code>VAL(x)</code>.

}}

[[Category:Manipulation]]

ITERATE - Revision history

Jrheinlaender at 19:38, 26 September 2024

Jrheinlaender at 16:31, 1 November 2017

Jrheinlaender at 14:27, 2 July 2017

Jrheinlaender at 19:22, 27 June 2017

Jrheinlaender: Created page with "{{Keyword | 1= ITERATE ( equation, expression, expression, integer ) ITERATE (equation list, expression list, expression list, inte..."

Jrheinlaender: Created page with "{{Keyword | 1= `ITERATE ( equation, expression, expression, integer )` `ITERATE (equation list, expression list, expression list, inte..."`