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# Automatic Method for Deciding the Convergence of Numerical Integration

IP.com Disclosure Number: IPCOM000116282D
Original Publication Date: 1995-Aug-01
Included in the Prior Art Database: 2005-Mar-30
Document File: 2 page(s) / 38K

IBM

## Related People

Tezuka, S: AUTHOR

## Abstract

Disclosed is an automatic method for deciding the convergence of numerical integration based on low-discrepancy sequences. The key ideas included in this disclosure are as follows: 1. The algorithm uses several different classes of low-discrepancy sequences. 2. The convergence is decided based on the difference between these different classes of low-discrepancy sequences.

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Automatic Method for Deciding the Convergence of Numerical Integration

Disclosed is an automatic method for deciding the convergence
of numerical integration based on low-discrepancy sequences.  The key
ideas included in this disclosure are as follows:
1.  The algorithm uses several different classes of low-discrepancy
sequences.
2.  The convergence is decided based on the difference between
these
different classes of low-discrepancy sequences.

The Figure shows the example of this algorithm.  This example
employs two different classes of low-discrepancy sequences.  Thus,
the Figure contains two different numerical results of integration.
The x-axis means the number of sample points.  The y-axis means the
value of integration.  As the number of samples grows, the value of
integration converges for each of two cases of computation.  Given a
prespecified threshold, T, and the period length, P, the algorithm
decides the convergence of the computation as follows: If the
difference between the integration values of two computations is less
than T during the period P, the algorithm decides that the numerical
integration has converged.  In this example, the convergence is