MATLAB: How to get improper fraction representation from rat(x,tol) function

rational

Dear matlab forum,

Hello. the rat(x,tol) function outputs a string of a continued fraction, for example '5+1/(7+1/4)'. How can I condense this into an improper fraction of only one numerator and denominator?

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[N,D] = rat(x,tol);

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MATLAB: AbsTol, RelTol

The absolute tolerance of 1e-3 is meaningless, when the values are very small, e.g. 1.234e-27. Then the relative tolerance is more useful.

The precision of the result is IEEE-64bit double in every case, but the accuracy is influenced by the tolerances. The tolerances are used to limit the local discretization error: If the difference between a high-accuracy and low-accuracy integration is higher than one of the tolerances, the step size is reduced.

If the tolerance is too low, the large number of steps will increase the accumulated rounding errors, while for a to high tolerance the local discretization errors dominate the accuracy of the result.

MATLAB: Does the RAT function not return the smallest possible numerator and denominator for a given floating point number

The RAT function will give values for the numerator and denominator that are within the specified tolerance and does not guarantee that the numbers returned are the smallest possible set of numerator and denominator values.

When you supply a tolerance, you are telling the RAT function when the approximation is good enough to quit. There is no guarantee that the approximation returned will have the smallest numerator and denominator possible when the sequence is terminated. The algorithm does not consider all possibilities, rather a subset of possibilities that are constructed in a certain way.

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Related Solutions

MATLAB: AbsTol, RelTol

MATLAB: Does the RAT function not return the smallest possible numerator and denominator for a given floating point number

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