This question has been asked before, but I have been asked yet again to recommend reliable books on high-quality, modern algorithms for numerical tasks. Ideally, fairly general ones, but ones for specific fields would also be useful. They should also be implementable in Fortran - i.e. should NOT require dynamic compilation, no type checking and other such aberrations.
By "reliable, high-quality, modern", I mean an order of magnitude better than Numerical Recipes, of course.
Any suggestions appreciated, but I am not optimistic :-(
> This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful. They should also be implementable in > Fortran - i.e. should NOT require dynamic compilation, no type > checking and other such aberrations.
> By "reliable, high-quality, modern", I mean an order of magnitude > better than Numerical Recipes, of course.
> Any suggestions appreciated, but I am not optimistic :-(
> Regards, > Nick Maclaren.
I'm curious...
What do you think are the books containing a) reliable b) reliable, high-quality c) reliable, high-quality, modern algorithms for numerical tasks?
>What do you think are the books containing >a) reliable >b) reliable, high-quality >c) reliable, high-quality, modern >algorithms for numerical tasks?
>I'm not trying to bother you, I'm really curious.
There are a fair number of those that hit the first two: one classic is Wilkinson and Reinsch "The Algebraic Eigenvalue Problem". Or even Acton "Numerical Methods that Work".
n...@cam.ac.uk wrote: > In article<fce59157-bf4d-4b7c-b31a-5ca174d5e...@u24g2000prn.googlegroups.com>, > gmail-unlp<ftine...@gmail.com> wrote:
>> I'm curious...
>> What do you think are the books containing >> a) reliable >> b) reliable, high-quality >> c) reliable, high-quality, modern >> algorithms for numerical tasks?
>> I'm not trying to bother you, I'm really curious.
> There are a fair number of those that hit the first two: one classic > is Wilkinson and Reinsch "The Algebraic Eigenvalue Problem". > Or even Acton "Numerical Methods that Work".
I love Acton, but he's hardly got half a dozen algorithms in the whole book! It's much more of a lore book than an algorithm book.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal ElectroOptical Innovations 55 Orchard Rd Briarcliff Manor NY 10510 845-480-2058
> >What do you think are the books containing > >a) reliable > >b) reliable, high-quality > >c) reliable, high-quality, modern > >algorithms for numerical tasks?
> >I'm not trying to bother you, I'm really curious.
> There are a fair number of those that hit the first two: one classic > is Wilkinson and Reinsch "The Algebraic Eigenvalue Problem". > Or even Acton "Numerical Methods that Work".
> Regards, > Nick Maclaren.
Thanks. I use "Matrix Computations" by Golub and van Loan as a reference in linear algebra, it includes symmetric and unsymmetric Eigenvalue problems.
> This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful.
I can recommend
Goloub & van Loan (1996) Matrix Computations. Johns Hopkins University Press.
for anything that deals with linear algebra.
Algorithms from pseudo-code can easily be implemented in Fortran 95. It has references to LAPACK and BLAS routines, and some material on MPI-style parallel algorithms.
> This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful. They should also be implementable in > Fortran - i.e. should NOT require dynamic compilation, no type > checking and other such aberrations.
> By "reliable, high-quality, modern", I mean an order of magnitude > better than Numerical Recipes, of course.
> Any suggestions appreciated, but I am not optimistic :-(
I would recommend "Introduction to Numerical Analysis" by F.B. Hildebrand. The only caveat is that there is not an ort of "computer code" in the book. It contains just math and algorithms.
The Collected Algorithms of ACM was available in book volumes, some with and some without microfiche, and most algorithms were in Fortran. I am unaware of the current availability in book form but I see that some algorithms are downloadable at http://calgo.acm.org/ .
> This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful. They should also be implementable in > Fortran - i.e. should NOT require dynamic compilation, no type > checking and other such aberrations.
> By "reliable, high-quality, modern", I mean an order of magnitude > better than Numerical Recipes, of course.
> Any suggestions appreciated, but I am not optimistic :-(
> The Collected Algorithms of ACM was available in book volumes, some > with and some without microfiche, and most algorithms were in > Fortran. I am unaware of the current availability in book form but I > see that some algorithms are downloadable athttp://calgo.acm.org/.
> > This question has been asked before, but I have been asked yet again > > to recommend reliable books on high-quality, modern algorithms for > > numerical tasks. Ideally, fairly general ones, but ones for specific > > fields would also be useful. They should also be implementable in > > Fortran - i.e. should NOT require dynamic compilation, no type > > checking and other such aberrations.
> > By "reliable, high-quality, modern", I mean an order of magnitude > > better than Numerical Recipes, of course.
> > Any suggestions appreciated, but I am not optimistic :-(
> > Regards, > > Nick Maclaren.- Hide quoted text -
> >What do you think are the books containing > >a) reliable > >b) reliable, high-quality > >c) reliable, high-quality, modern > >algorithms for numerical tasks?
> >I'm not trying to bother you, I'm really curious.
> There are a fair number of those that hit the first two: one classic > is Wilkinson and Reinsch "The Algebraic Eigenvalue Problem". > Or even Acton "Numerical Methods that Work".
I was going to mention Acton until I scanned the replies and saw this mention already made.
Of course, you left out the part of the title that is hard to cite well in a purely textual form: the "usually" that is highlighted on the cover by the embossing of slected letters in the rest of the title.
I suppose you are right that it is not particularly modern. But it is still worth reading.
-- Richard Maine | Good judgment comes from experience; email: last name at domain . net | experience comes from bad judgment. domain: summertriangle | -- Mark Twain
In comp.lang.fortran n...@cam.ac.uk wrote: > This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful. They should also be implementable in > Fortran - i.e. should NOT require dynamic compilation, no type > checking and other such aberrations. > By "reliable, high-quality, modern", I mean an order of magnitude > better than Numerical Recipes, of course. > Any suggestions appreciated, but I am not optimistic :-(
I don't believe that you can fit into a book the breadth of coverage of NR, and at significantly more depth. (Quality is likely not linear with depth (pages), so maybe only two or three times the pages.)
As I remember it, NR supplies references for more depth on each specific topic (more or less chapter). If you go down the list and select about 10 of them, (you probably recognize the names), you should have a high quality library of numerical methods books.
Though it seems usual for the deeper books to be more theory and less practice (sample code).
> This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful. They should also be implementable in > Fortran - i.e. should NOT require dynamic compilation, no type > checking and other such aberrations.
Why prohibit type checking? Fortran 90 code with modules or interfaces has it.
Beliavsky <beliav...@aol.com> wrote: > On Feb 24, 8:35 am, n...@cam.ac.uk wrote: > > This question has been asked before, but I have been asked yet again > > to recommend reliable books on high-quality, modern algorithms for > > numerical tasks. Ideally, fairly general ones, but ones for specific > > fields would also be useful. They should also be implementable in > > Fortran - i.e. should NOT require dynamic compilation, no type > > checking and other such aberrations.
> Why prohibit type checking? Fortran 90 code with modules or interfaces > has it.
The wording is slightly awkward. I had to read it a second time myself because it didn't seem to make sense the first time. But if I read it correctly on the second pass, I think you missed the double negative; that is, it should NOT require no type checking.
-- Richard Maine | Good judgment comes from experience; email: last name at domain . net | experience comes from bad judgment. domain: summertriangle | -- Mark Twain
>> On Feb 24, 8:35 am, n...@cam.ac.uk wrote: >>> This question has been asked before, but I have been asked yet again >>> to recommend reliable books on high-quality, modern algorithms for >>> numerical tasks. Ideally, fairly general ones, but ones for specific >>> fields would also be useful. They should also be implementable in >>> Fortran - i.e. should NOT require dynamic compilation, no type >>> checking and other such aberrations.
>> Why prohibit type checking? Fortran 90 code with modules or interfaces >> has it.
> The wording is slightly awkward. I had to read it a second time myself > because it didn't seem to make sense the first time. But if I read it > correctly on the second pass, I think you missed the double negative; > that is, it should NOT require no type checking.
I inferred the wording was specifically aimed at rejecting the texts written with the Matlab's of the world in mind...
dpb <n...@non.net> wrote: >On 2/24/2011 1:51 PM, Richard Maine wrote: >> Beliavsky<beliav...@aol.com> wrote:
>>>> This question has been asked before, but I have been asked yet again >>>> to recommend reliable books on high-quality, modern algorithms for >>>> numerical tasks. Ideally, fairly general ones, but ones for specific >>>> fields would also be useful. They should also be implementable in >>>> Fortran - i.e. should NOT require dynamic compilation, no type >>>> checking and other such aberrations.
>>> Why prohibit type checking? Fortran 90 code with modules or interfaces >>> has it.
>> The wording is slightly awkward. I had to read it a second time myself >> because it didn't seem to make sense the first time. But if I read it >> correctly on the second pass, I think you missed the double negative; >> that is, it should NOT require no type checking.
>I inferred the wording was specifically aimed at rejecting the texts >written with the Matlab's of the world in mind...
I apologise for being gratuitously obfuscatory!
As Richard has pointed out before, I tend to think and write in double negatives a bit much for clear communication. I was trying to say that the books should be compatible with implementation in Matlab or straightforward Fortran.
There are occasional books that assume an unchecked language, or one with dynamic typing, and they are murder to implement in languages with strong, usually static, typing. The same is true of the ones that assume that code can be created and executed dynamically.
>This question has been asked before, but I have been asked yet again >to recommend reliable books on high-quality, modern algorithms for >numerical tasks. Ideally, fairly general ones, but ones for specific >fields would also be useful. They should also be implementable in >Fortran - i.e. should NOT require dynamic compilation, no type >checking and other such aberrations.
>By "reliable, high-quality, modern", I mean an order of magnitude >better than Numerical Recipes, of course.
"Accuracy and Stability of Numerical Algorithms" by Nicholas Higham
(I have the second edition, published by SIAM in 2002). Of course its scope is somewhat limited, but it has a lot of rather up-to-date references to modern methods in addition to extensive error analysis etc. It is unfortunately also quite expensive (> 55 EUR).
> This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful. They should also be implementable in > Fortran - i.e. should NOT require dynamic compilation, no type > checking and other such aberrations.
> By "reliable, high-quality, modern", I mean an order of magnitude > better than Numerical Recipes, of course.
> Any suggestions appreciated, but I am not optimistic :-(
Thank you everyone for your suggestions. None of them are what the questioner asked for, but all well worth pointing people at; it is a great help to know what classics are still available. Nick Higham's seems to be the only newcomer :-) I now need to do some serious reading and rereading, to remind myself what I should advise these books for - and see if I have shelf space for any!
My problem here, which other people will recognise, is that far too many students nowadays don't want understanding - they want recipes. This does not fit well with numerical computation of real problems, especially the non-trival ones :-(
Sparse matrices are again not one my areas, but there should be a new version of Duff, Erisman and Reid "Direct Methods for Sparse Matrices" shortly. I think that we can guarantee that the book will be Fortran-friendly :-)
In comp.lang.fortran n...@cam.ac.uk wrote: > This question has been asked before, but I have been asked yet again > to recommend reliable books on high-quality, modern algorithms for > numerical tasks. Ideally, fairly general ones, but ones for specific > fields would also be useful. They should also be implementable in > Fortran - i.e. should NOT require dynamic compilation, no type > checking and other such aberrations.
