rombquad

Performs Romberg quadrature.

Description

I noticed that the two Romberg quadrature functions on the FEX are identical (#34 and #8199). I increased the speed of the calculations for some integrations and simplified the algorithm to use a vector instead of a matrix for the interpolations.

See help for an example

Email me with bugs please. Thanks.

Acknowledgements

Rombint.M inspired this file.

• MATLAB release: MATLAB 7.0.1 (R14SP1)

[M. Lamb]

Note: submission #8199, which is mentioned in the description, has been removed due to clear plagiarism of its "plagi-author" Ahmad Colahi Damirchidaraci.

[Andy G.]

 

[Alan Peterson]

This function is excellent. Good job.

[Anne Howard]

Works well, this is a classic form of numerical integration that should come standard in Matlab.

[matt fig (author)]

Also, the updated (1-16) code has a call to fcnchk that will stall some of the algorithm speed. This was placed so a user could use a non 'vectorized' code. Thanks.

[John D'Errico]

Further investigation suggests that the lack of significant difference that I saw between this code and either of its replicated antecendents was apparently due to a less sophisticated JIT acceleration in my Matlab release. Newer releases than mine (R14, SP1, on the Mac) will hopefully see a speed enhancement. Older releases may not see any gain.

[John D'Errico]

A quick test showed no significant difference between this code and either of its replicated antecedents, either in time or accuracy. Plus, this version has only a number of iterations to control the resultant accuracy. This is far less understandable to the user than a number of decimal digits.