You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
The default algorithm for low n is now forward recurrence because the weights in Golub-Welsh become exactly zero long before they should underflow #52 . The corresponding functions laguerreRec and laguerreRecDer can be called with BigFloats and this can be extended to gausslaguerre.jl as well if for example besselroots.jl can handle BigFloats #22 .
method="RH" is removed such that the code is a lot shorter and the function polyAsyRHgen can still be called if expansions of corresponding orthogonal polynomials are needed: I can change the normalisation to something standard if required.
The timings mentioned in README.md should be repeated on the reference machine, as the explicit expansions are extremely fast: for example, the six Newton iterations required to compute t seem to take more than half the total execution time of gausslaguerre. Higher-order asymptotics were not implemented in the Airy region (currently only O(n^{-4}) for the nodes and O(n^{-2/3}) for the weights) as the latter easily underflow, like the subsampled quadrature rule in reference [7]. I plan to do something similar for Jacobi (, Legendre) and Hermite, and to make a pull request to chebfun then.
There has been some progress on this pull request. A lot of memory allocations were removed, some still remain in the evaluation of special functions (these could be removed by implementing an alternative evaluation method). Even without those, this is a lot faster than the previous implementation without explicit expansions.
The code for more generalized weight functions was moved to gaussfreud.jl, since the generalizations correspond to Freud-type weights (exp(-x^m) for m greater than 1).
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
The default algorithm for low n is now forward recurrence because the weights in Golub-Welsh become exactly zero long before they should underflow #52 . The corresponding functions laguerreRec and laguerreRecDer can be called with BigFloats and this can be extended to gausslaguerre.jl as well if for example besselroots.jl can handle BigFloats #22 .
method="RH" is removed such that the code is a lot shorter and the function polyAsyRHgen can still be called if expansions of corresponding orthogonal polynomials are needed: I can change the normalisation to something standard if required.
The timings mentioned in README.md should be repeated on the reference machine, as the explicit expansions are extremely fast: for example, the six Newton iterations required to compute t seem to take more than half the total execution time of gausslaguerre. Higher-order asymptotics were not implemented in the Airy region (currently only O(n^{-4}) for the nodes and O(n^{-2/3}) for the weights) as the latter easily underflow, like the subsampled quadrature rule in reference [7]. I plan to do something similar for Jacobi (, Legendre) and Hermite, and to make a pull request to chebfun then.