Your comments
Sorry for misunderstanding.
It is good idea to measure toolbox timings for different level of precision (actually we do this internally, but don't publish as our website is already over-filled with tables). But again, only for the case of extended precision, not double.
I think, in the world of arbitrary precision software we need to use different "well-known comparison point".
Probably toolbox might be the one since now it is the fastest among 3M (Maple, Matlab and Mathematica) :).
Double precision is implemented in hardware, extended in software. Slowdown factor might be as high as 100-1000.
It is good idea to measure toolbox timings for different level of precision (actually we do this internally, but don't publish as our website is already over-filled with tables). But again, only for the case of extended precision, not double.
I think, in the world of arbitrary precision software we need to use different "well-known comparison point".
Probably toolbox might be the one since now it is the fastest among 3M (Maple, Matlab and Mathematica) :).
Double precision is implemented in hardware, extended in software. Slowdown factor might be as high as 100-1000.
Now toolbox has new engine for basic array manipulation operations, see http://goo.gl/mBJrk7
Basically it is up to 4 times faster (2 in average). Hopefully this be useful.
Basically it is up to 4 times faster (2 in average). Hopefully this be useful.
This function has been added to toolbox.
Toolbox is not meant to replace the double precision computations.
Extended precision provided in toolbox is targeted to solve problems, which are not solvable in double precision (sensitive eigenvalues, ill-conditioned systems, etc.).
What comparison is possible here ;)? Solved / Not solved?
Speed is irrelevant if problem is not solved, right?
Extended precision provided in toolbox is targeted to solve problems, which are not solvable in double precision (sensitive eigenvalues, ill-conditioned systems, etc.).
What comparison is possible here ;)? Solved / Not solved?
Speed is irrelevant if problem is not solved, right?
That is because toolbox switches to multiprecision mode (if necessary) - to compute the bessel accurately.
Now toolbox is using adaptive algorithm for series summation - every operation is analysed for cancellation/rounding errors.
If it is of unacceptable level - precision is boosted up to compensate the issue. At the end we re-arrange the terms to guarantee the minimum accuracy loss overall [1].
It will became much faster in future, when we will add asymptotics for large arguments and (probably) simplify the algorithm.
Hope it is useful for your work.
Btw, our system solver has been updated today with faster decompositions under the hood. You might see some changes in computing time.
[1]. J. Demmel. Y. Hida. Fast and accurate floating point summation with application to computational geometry.
Now toolbox is using adaptive algorithm for series summation - every operation is analysed for cancellation/rounding errors.
If it is of unacceptable level - precision is boosted up to compensate the issue. At the end we re-arrange the terms to guarantee the minimum accuracy loss overall [1].
It will became much faster in future, when we will add asymptotics for large arguments and (probably) simplify the algorithm.
Hope it is useful for your work.
Btw, our system solver has been updated today with faster decompositions under the hood. You might see some changes in computing time.
[1]. J. Demmel. Y. Hida. Fast and accurate floating point summation with application to computational geometry.
Compilation for Windows just has been finished: http://goo.gl/jcoexM
Would appreciate your feedback.
Would appreciate your feedback.
Customer support service by UserEcho
I think the fastest way would be to just compare particular algorithm(s) of interest.
Toolbox trial is full functional and has all the optimizations - it can be downloaded from our website and run in a few minutes.