Derivative - Revision history

WikiSysop: /* Forward and Backward Differencing */

2021-08-26T13:39:16Z

Forward and Backward Differencing

← Older revision		Revision as of 09:39, 26 August 2021
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	==Forward and Backward Differencing==		==Forward and Backward Differencing==

	Central Differencing samples points on both sides of a center point which works fine for a function everywhere defined. However if you need a derivative of a function undefined below a certain point and you need the derivative at or near that point, Central Differencing won’t work.		Central Differencing samples points on both sides of a center point which works fine for a function everywhere defined. However if you need a derivative of a function undefined above or below a certain point and you need the derivative at or near that point, Central Differencing won’t work.

	Forward differencing samples the values of the function at or above the given point, never below. For example, in the set of Real numbers, the square root of X is undefined below <apll>0</apll>, and so if you want to calculate a derivative of that function at <apll>0</apll>, you’ll need Forward Differencing. Backward Differencing is simply the dual to Forward Differencing.		Forward differencing samples the values of the function at or above the given point, never below. For example, in the set of Real numbers, the square root of X is undefined below <apll>0</apll>, and so if you want to calculate a derivative of that function at <apll>0</apll>, you’ll need Forward Differencing. Backward Differencing is simply the dual to Forward Differencing.

WikiSysop: /* Accuracy */

2021-08-26T00:44:21Z

Accuracy

← Older revision		Revision as of 20:44, 25 August 2021
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	I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:		I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:

	[[~~file~~:deriv1.jpg]]		[[File:deriv1.jpg]]

	==Classification==		==Classification==

WikiSysop: /* Accuracy */

2021-08-26T00:43:30Z

Accuracy

← Older revision		Revision as of 20:43, 25 August 2021
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	I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:		I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:

	[[file:~~/art/~~deriv1.jpg]]		[[file:deriv1.jpg]]

	==Classification==		==Classification==

WikiSysop: /* Accuracy */

2021-08-26T00:43:14Z

Accuracy

← Older revision		Revision as of 20:43, 25 August 2021
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	I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:		I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:

	[[~~image~~:/art/deriv1.jpg]]		[[file:/art/deriv1.jpg]]

	==Classification==		==Classification==

WikiSysop: /* Accuracy */

2021-08-26T00:41:24Z

Accuracy

← Older revision		Revision as of 20:41, 25 August 2021
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	I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:		I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:

	[[/art/deriv1.jpg]]		[[image:/art/deriv1.jpg]]

	==Classification==		==Classification==

WikiSysop: /* Accuracy */

2021-08-26T00:40:55Z

Accuracy

← Older revision		Revision as of 20:40, 25 August 2021
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	I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:		I became convinced that this algorithm was worth investigating when I saw the following “worth a thousand words” picture in the original<ref name="NewFinite"/> paper:

	[[~~image:~~deriv1.jpg]]		[[/art/deriv1.jpg]]

	==Classification==		==Classification==

WikiSysop: /* Partial Derivatives */

2020-05-03T18:08:20Z

Partial Derivatives

← Older revision		Revision as of 14:08, 3 May 2020
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	In APL, we don't have multiple variables, but we do have multiple elements in an array argument to the Derivative operator where the function Operand also returns multiple values. This concept is explained more clearly in Iverson<ref name="IversonDerivative"/> and		In APL, we don't have multiple variables, but we do have multiple elements in an array argument to the Derivative operator where the function Operand also returns multiple values. This concept is explained more clearly in Iverson<ref name="IversonDerivative"/> and
	Powell<ref name="PowellDerivative">"The Derivative Revisited", Mike Powell[https://~~www.scribd~~.com/~~document~~/~~422558534~~/~~The-Derivative-Revisited~~]</ref>.		Powell<ref name="PowellDerivative">"The Derivative Revisited", Mike Powell[https://aplwiki.com/images/f/f9/1_The_Derivative_Revisited.pdf]</ref>.

	For example, from Iverson<ref name="IversonDerivative"/>,		For example, from Iverson<ref name="IversonDerivative"/>,

WikiSysop at 00:59, 8 April 2020

2020-04-08T00:59:12Z

← Older revision		Revision as of 20:59, 7 April 2020
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	While working on the Matrix operator<ref name="MatrixOperator">NARS2000 Wiki, "Matrix Operator" [http://wiki.nars2000.org/index.php/Matrix]</ref>, I’ve found I needed a Numerical Differentiation (ND) operator in order to apply the Matrix operator to non-diagonalizable matrices. This operator uses Numerical Analysis methods to calculate the value of the Derivative of a function at a given point.		While working on the Matrix operator<ref name="MatrixOperator">NARS2000 Wiki, "Matrix Operator" [http://wiki.nars2000.org/index.php/Matrix]</ref>, I’ve found I needed a Numerical Differentiation (ND) operator in order to apply the Matrix operator to non-diagonalizable matrices. This operator uses Numerical Analysis methods to calculate the value of the Derivative of a function at a given point.

	It may be used to calculate Nth order Derivatives as well as first order Partial Derivatives. The latter are calculated as per Iverson<ref name="IversonDerivative">APL '79: Proceedings of the international conference on APL: part 1, May 1979, pp. 347–354[https://doi.org/10.1145/800136.804486]</ref> and expanded upon by Powell<ref name="PowellDerivative"/>.		It may be used to calculate Nth order Derivatives as well as first order Partial Derivatives. The latter are calculated as per Iverson<ref name="IversonDerivative">"The Derivative Operator", Kenneth E. Iverson, APL '79: Proceedings of the international conference on APL: part 1, May 1979, pp. 347–354[https://doi.org/10.1145/800136.804486]</ref> and expanded upon by Powell<ref name="PowellDerivative"/>.

	==Notation==		==Notation==
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	In APL, we don't have multiple variables, but we do have multiple elements in an array argument to the Derivative operator where the function Operand also returns multiple values. This concept is explained more clearly in Iverson<ref name="IversonDerivative"/> and		In APL, we don't have multiple variables, but we do have multiple elements in an array argument to the Derivative operator where the function Operand also returns multiple values. This concept is explained more clearly in Iverson<ref name="IversonDerivative"/> and
	Powell<ref name="PowellDerivative">~~Mike Powell,~~ The Derivative Revisited[https://www.scribd.com/document/422558534/The-Derivative-Revisited]</ref>.		Powell<ref name="PowellDerivative">"The Derivative Revisited", Mike Powell[https://www.scribd.com/document/422558534/The-Derivative-Revisited]</ref>.

	For example, from Iverson<ref name="IversonDerivative"/>,		For example, from Iverson<ref name="IversonDerivative"/>,

WikiSysop: /* Partial Derivatives */

2020-04-08T00:55:07Z

Partial Derivatives

← Older revision		Revision as of 20:55, 7 April 2020
Line 224:		Line 224:

	In APL, we don't have multiple variables, but we do have multiple elements in an array argument to the Derivative operator where the function Operand also returns multiple values. This concept is explained more clearly in Iverson<ref name="IversonDerivative"/> and		In APL, we don't have multiple variables, but we do have multiple elements in an array argument to the Derivative operator where the function Operand also returns multiple values. This concept is explained more clearly in Iverson<ref name="IversonDerivative"/> and
	Powell<ref name="PowellDerivative"> The Derivative Revisited[https://www.scribd.com/document/422558534/The-Derivative-Revisited]</ref>.		Powell<ref name="PowellDerivative">Mike Powell, The Derivative Revisited[https://www.scribd.com/document/422558534/The-Derivative-Revisited]</ref>.

	For example, from Iverson<ref name="IversonDerivative"/>,		For example, from Iverson<ref name="IversonDerivative"/>,

WikiSysop: /* Introduction */

2020-04-08T00:54:17Z

Introduction

← Older revision		Revision as of 20:54, 7 April 2020
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	While working on the Matrix operator<ref name="MatrixOperator">NARS2000 Wiki, "Matrix Operator" [http://wiki.nars2000.org/index.php/Matrix]</ref>, I’ve found I needed a Numerical Differentiation (ND) operator in order to apply the Matrix operator to non-diagonalizable matrices. This operator uses Numerical Analysis methods to calculate the value of the Derivative of a function at a given point.		While working on the Matrix operator<ref name="MatrixOperator">NARS2000 Wiki, "Matrix Operator" [http://wiki.nars2000.org/index.php/Matrix]</ref>, I’ve found I needed a Numerical Differentiation (ND) operator in order to apply the Matrix operator to non-diagonalizable matrices. This operator uses Numerical Analysis methods to calculate the value of the Derivative of a function at a given point.

	It may be used to calculate Nth order Derivatives as well as first order Partial Derivatives. The latter are calculated as per Iverson<ref name="IversonDerivative">APL '79: Proceedings of the international conference on APL: part 1, May 1979, pp. 347–354[https://doi.org/10.1145/800136.804486]</ref>.		It may be used to calculate Nth order Derivatives as well as first order Partial Derivatives. The latter are calculated as per Iverson<ref name="IversonDerivative">APL '79: Proceedings of the international conference on APL: part 1, May 1979, pp. 347–354[https://doi.org/10.1145/800136.804486]</ref> and expanded upon by Powell<ref name="PowellDerivative"/>.

	==Notation==		==Notation==