I thought that some participants here might find Bill Press’s account of the writing and reception of the Numerical Recipes book of interest. See: chapter 42 at http://morethancurious.com/reader/](http://morethancurious.com/reader/). There is a lesson here for programmers to “meet users where they are”.
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This was also discussed in Anecdotal Fortran... :-) - #327 by Beliavsky and a few following posts.
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For a different view of Numerical Recipes, people should read the various comments from Numerical Methods researchers about NR compiled by Van Snyder (who I believe was at one time a member of the Standards Committee, maybe still is)
https://www.stat.uchicago.edu/~lekheng/courses/302/wnnr/nr.html
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I was wondering when that review would make it in the thread. Can anyone recommend some Numerical methods texts worth study? I know there are a few open source texts:
There is also this numerical analysis book
FWIW, here is a positive review from the Mathematical Association of America
There are older books that cover the basics well – I don’t see how you could go wrong with Hamming’s Numerical Methods for Scientists and Engineers, but it is likely very dated at this point.
There is a list of recommendations (circa 2001) from the same website:
Alternatives to Numerical Recepies
I actually stopped using (and letting my students use) Numerical Recipe code before I found that review because of the restrictive license that was imposed on the code (even if you just reproduced it from the listings in the books). I also found a couple of routines (the SVD code in particular) were just a slightly reworked versions of the code in Forsythe, Malcom, and Molers classic text " Computer Methods for Mathematical Computation"
which is still a nice book after all these years if you can find a copy.
Dalquist and Bjorck have newer versions of their classic Numerical Methods book.
https://epubs.siam.org/doi/book/10.1137/1.9780898717785
I can also recommend the Fortran version of Engeln-Mullges and Uhlig’s Numerical Algorithms book
The source code for the algorithms they cover is available as extra material from the publisher but you might have to look around for it.
Edit: The source code for the Engeln_Mullges and Uhlig book is available here.
https://storage.googleapis.com/springer-extras/zip/1996/978-3-642-80045-0.zip
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Searching “numerical” in my list of Fortran-related books gives
Antia, H.M. (2012). Numerical methods for scientists and engineers, 3rd ed. Hindustan Book Agency.
Bagirov, Adil, M. Gaudioso, N. Karmitsa, M. M. Mäkelä, and S. Taheri, (Eds.), (2020). Numerical Nonsmooth Optimization: State of the Art Algorithms. Springer
Bierman, Gerald J. (1977). Factorization Methods for Discrete Sequential Estimation Academic Press. (contains Fortran pseudo-code for numerically stable Kalman filters). The code in esl.tgz from Netlib does estimation and smoothing by UDU**T and square root information filter SRIF for Kalman filtering.
Bose, Sujit Kumar (2019). Numerical Methods of Mathematics Implemented in Fortran. Springer. reviewed here
Burden, Richard, L., J. Douglas Faires and Annette M. Burden (2016). Numerical Analysis, 10th ed.. Cengage. FORTRAN 77 code here
Cheney, Ward and David Kincaid (2012). Numerical Mathematics and Computing, 7th ed.. Brooks/Cole: Cengage Learning
Davis, Mark E. (1984). Numerical Methods & Modeling for Chemical Engineers. Wiley
Davis, Philip J., and Philip Rabinowitz (1984). Methods of Numerical Integration, 2nd. ed.. Academic Press
Dennis, Jr., J.E., and Robert B. Schnabel (1996). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM. Fortran 90 code for UNCMIN at Alan Miller’s site
Engeln-Müllges, Gisela and Uhlig, Frank (2013). Numerical Algorithms with Fortran. Springer.
Garcia, Alejandro L. (1994). Numerical Methods for Physics. Prentice Hall
Goedecker, Stefan, and Adolfy Hoisie (2001). Performance Optimization of Numerically Intensive Codes. SIAM. Codes here.
Griffiths, D. Vaughan, and I.M. Smith (2006). Numerical Methods for Engineers, 2nd ed.. CRC. Code at Griffiths’ site
Hager, William (1988). Applied Numerical Linear Algebra. Prentice Hall. NAPACK code at John Burkardt’s site
Knuth, Donald E. (1997). Seminumerical Algorithms, 3rd ed. Code here
Kagiwada, Harriet, Robert Kalaba, Nima Rasakhoo, and Karl Spingarn (1986). Numerical Derivatives and Nonlinear Analysis. Springer
Kahaner, David, Cleve Moler, and Stephen Nash (1998). Numerical Methods and Software. Prentice Hall. Fortran 90 code here
Kincaid, David and Ward Cheney (2002). Numerical Analysis: Mathematics of Scientific Computing, 3rd ed.. American Mathematical Society. Code here
Monahan, John F. (2011). Numerical Methods of Statistics, 2nd ed.. Cambridge University Press
Moursund, David G., and Charles S. Duris (1988). Elementary Theory and Application of Numerical Analysis. Dover
Nocedal, Jorge, and Stephen J. Wright (2006). Numerical Optimization. Springer. Related code at Nocedal’s site
Orlandi, Paolo (2000). Fluid Flow Phenomena: A Numerical Toolkit. Kluwer. Code at author’s site
Pozrikidis, C. (2017). Fluid Dynamics: Theory, Computation, and Numerical Simulation, 3rd ed.. Springer
Pozrikidis, C. (2008). Numerical Computation in Science and Engineering, 2nd. ed.. Oxford University Press
Press, Flannery, Teukolsky, and Vetterling (1992). Numerical Recipes in Fortran 77. Cambridge University Press.
Press, Teukolsky, Vetterling and Flannery (1996). Numerical Recipes in Fortran 90 - The Art of Parallel Scientific Computing. Cambridge University Press
Ramkarthik, M.S., and Payal D. Solanki (2021). Numerical Recipes in Quantum Information Theory and Quantum Computing: An Adventure in FORTRAN 90.
Ramos, Juan Antonio Hernandez, and Lopez, Javier Escoto (2020). How to learn Applied Mathematics through modern FORTRAN. Independently published code and text
Saad, Yousef (2011). Numerical Methods for Large Eigenvalue Problems - 2nd Edition. SIAM
Schiesser, W. E., and C. A. Silebi (1997). Computational Transport Phenomena: Numerical Methods for the Solution of Transport Problems. Cambridge University Press. Code here.
Schiesser, W. E. (1991). The Numerical Method of Lines: Integration of Partial Differential Equations 1st ed.. Academic Press
Schittkowski, Klaus (2002). Numerical Data Fitting in Dynamical Systems - A Practical Introduction with Applications and Software. Kluwer
Sewell, Granville (2015) The Numerical Solution of Ordinary and Partial Differential Equations, 3rd Ed.. World Scientific
Tikhonov, A.N., Goncharsky, A., Stepanov, V.V., and Yagola, A.G. (1995). Numerical Methods for the Solution of Ill-Posed Problems. Springer
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