c++ numerical analysis Accurate data structure?

Using double type I made Cubic Spline Interpolation Algorithm. That work was success as it seems, but there wa开发者_StackOverflow社区s a relative error around 6% when very small values calculated.

Is double data type enough for accurate scientific numerical analysis?

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Double has plenty of precision for most applications. Of course it is finite, but it's always possible to squander any amount of precision by using a bad algorithm. In fact, that should be your first suspect. Look hard at your code and see if you're doing something that lets rounding errors accumulate quicker than necessary, or risky things like subtracting values that are very close to each other.

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Scientific numerical analysis is difficult to get right which is why I leave it the professionals. Have you considered using a numeric library instead of writing your own? Eigen is my current favorite here: http://eigen.tuxfamily.org/index.php?title=Main_Page

I always have close at hand the latest copy of Numerical Recipes (nr.com) which does have an excellent chapter on interpolation. NR has a restrictive license but the writers know what they are doing and provide a succinct writeup on each numerical technique. Other libraries to look at include: ATLAS and GNU Scientific Library.

To answer your question double should be more than enough for most scientific applications, I agree with the previous posters it should like an algorithm problem. Have you considered posting the code for the algorithm you are using?

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If double is enough for your needs depends on the type of numbers you are working with. As Henning suggests, it is probably best to take a look at the algorithms you are using and make sure they are numerically stable.

For starters, here's a good algorithm for addition: Kahan summation algorithm.

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Double precision will be mostly suitable for any problem but the cubic spline will not work well if the polynomial or function is quickly oscillating or repeating or of quite high dimension.

In this case it can be better to use Legendre Polynomials since they handle variants of exponentials.

By way of a simple example if you use, Euler, Trapezoidal or Simpson's rule for interpolating within a 3rd order polynomial you won't need a huge sample rate to get the interpolant (area under the curve). However, if you apply these to an exponential function the sample rate may need to greatly increase to avoid loosing a lot of precision. Legendre Polynomials can cater for this case much more readily.