OpenMath Content Dictionary: numerical1

Canonical URL:

http://www.openmath.org/cd/numerical1.ocd

CD File:

numerical1.ocd

CD as XML Encoded OpenMath:

numerical1.omcd

Defines:

absolute_error_bound, absolute_error_requested, relative_error_bound, relative_error_requested

Date:

2003-09-16

Version:

1 (Revision 1)

Review Date:

2017-12-31

Status:

experimental

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          both this document and the derived work are Content Dictionaries
          then the derived work must include a different CDName element,
          chosen so that it cannot be confused with any works adopted by
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          Dictionary Group whose name is, for example, `math' containing
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          However you are free to name it `private_mathN' or some such.  This
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  Author: James Davenport

This CD contains descriptors of tolerances (errors) for numerical methods. Note that there are two kinds: the (input) request for a computation within a certain error bound, and an (output) estimated bound for the error. Either kind can be relative or absolute. While it would be normal to respond to a relative_error_requested with a relative_error_bound, this might be meaningless if |computed| is small, so an absolute_error-bound might be the right response.

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absolute_error_requested

Description:

This symbol marks a requirement for the absolute error ( |true-computed| ) on a computation.

Example:

OpenMath XML (source)

         <OMOBJ xmlns="http://www.openmath.org/OpenMath">
	   <OMA>
	     <OMS name="absolute_error_requested" cd="numerical1"/>
	     <OMF dec="1.0e-6"/>
	   </OMA>
         </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol cd="numerical1">absolute_error_requested</csymbol><cn type="real">1.0e-6</cn></apply></math>

Prefix

absolute_error_requested ( 1.0e-6 )

Popcorn

numerical1.absolute_error_requested(1.0e-6)

Rendered Presentation MathML

$$\mathrm{absolute\_error\_requested}\left(1.0e-6\right)$$

Signatures:

sts

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[Next: relative_error_requested] [Last: relative_error_bound] [Top]

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relative_error_requested

Description:

This symbol marks a requirement for the relative error ( |true-computed|/|computed| ) on a computation.

Signatures:

sts

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[Next: absolute_error_bound] [Previous: absolute_error_requested] [Top]

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absolute_error_bound

Description:

This symbol marks an estimated upper bound for the absolute error ( |true-computed| ) on a computation.

Signatures:

sts

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[Next: relative_error_bound] [Previous: relative_error_requested] [Top]

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relative_error_bound

Description:

This symbol marks an estimated upper bound for the relative error ( |true-computed|/|computed| ) on a computation.

Signatures:

sts

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[First: absolute_error_requested] [Previous: absolute_error_bound] [Top]