Re: Intervalar Mathematics with Octave

[Przemek Klosowski]

Oscar <address@hidden> asked:

   > I need a interval mathematic to use with octave, does it exist?

Interval arithmetics (IA) is a method to get an error estimate of a
numerical computation by specifying the input variables as confidence
intervals and recalculating the confidence interval alongside the
calculation, e.g. instead of 3/0.1 we'd do [2.99 3.01] / [.09 .11] and
the result would be [27.18 33.44].

Interval arithmetic captures roundoff, precision, and other numerical
errors, as well as some algorithmic errors, like calculating
near/across a branch cut. There were efforts to design both IA
hardware and to instrument compilers to generate IA calculations for
regular floating point code. There are two problems:

 - speed: IA at least doubles the number of FP calculations needed

 - accuracy: IA assumes independence of all input terms, and therefore
   IA estimates of confidence intervals tend to blow up: [0 Inf] is a
   technically correct but not very useful result.

Octave doesn't do interval arithmetic directly. You could do them by
hand or use Octave (or external) symbolic computing to get the
derivatives of your expressions, and use the error propagation rules
dy = (dy/dx) dx.