Looking for good book on Numerical Methods and/or Optimization

Click For Summary

Discussion Overview

The discussion centers around recommendations for books on Numerical Methods and Optimization, with a focus on resources that bridge theory and practical implementation. Participants express preferences for books that include worked examples and are not overly theoretical, while also seeking specific topics like Singular Value Decomposition (SVD) and various optimization techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant emphasizes the need for worked examples and a practical approach, expressing a preference for books that do not require deep mathematical understanding.
  • Another participant suggests "Schaum's Outline" as a suitable option that meets the criteria for practical examples.
  • A different participant recommends "Practical Optimization Methods" by Bhatti, highlighting its focus on implementation with Mathematica and its coverage of various optimization problem categories.
  • Several participants mention "Numerical Recipes" in various programming languages as a potential resource.
  • One participant points to a free online book by Boyd on optimization, noting its abundance of examples.
  • Another participant recommends a book by Trefethen for its intuitive presentation of smaller numerical techniques, including SVD.
  • A link to a paper on iterative system solvers is shared, praised for its visual explanations.

Areas of Agreement / Disagreement

Participants express a variety of preferences and suggestions, indicating that there is no consensus on a single best resource. Multiple competing views on suitable books remain, with some participants favoring specific titles while others seek additional recommendations.

Contextual Notes

Some participants mention the need for books that balance theory and practical application, but specific assumptions about the depth of mathematical content are not universally agreed upon. There are also references to classic texts in related fields, but no definitive classics in Numerical Methods or Optimization are established in this discussion.

Who May Find This Useful

Readers interested in Numerical Methods and Optimization, particularly those looking for practical resources with worked examples and accessible explanations.

hotvette
Homework Helper
Messages
1,001
Reaction score
11
Any recommendations? The books I have are very outdated. Extremely important to me are:

- worked examples #1 criteria. Need that bridge between theory and implementation.

- not overly heavy on theory (don't want to hire a PhD to explain it). I have an MS Engineering level education (PDE's was the last math class I took).

- would love the book to include Singular Value Decomposition (SVD) and Optimization techniques, though I have a feeling that a good treatment of Optimization would need to be in a separate book

Appreciate any/all suggestions. Thanks! :-p
 
Last edited:
Physics news on Phys.org
Schaums outline isn't too bad, fits criteria #1 very well.
 
OMG, I had totally forgotten about Schaums. Seems like a lifetime ago (sorta was, actually). On the way courtesy of Amazon. Thanks.

In the meantime, I'd like to re-phrase my question and request additional replies.

Are there any Numerical Methods or Optimization books that you absolutely love (or like a lot)? If, so I'd appreciate the title/author/edition and comments as to why.

Thanks :smile:
 
Keeping in mind #1 & and not going 'too deep' in math how about "Practical Optimization Methods" by Bhatti. It's pretty recent and the whole book is written with mathematica implementations in mind (contains a CD of the stuff)(similar books exist if going to use for example MATLAB as a platform, but don't have experience about those). What I like about it in particular is that it presents recent methods for a wide variety of different numerical optimization problem 'categories' and it's heavy with respect to the implementation aspect (and tolerable if you like to avoid "excess" math).
 
Numerical Recipes in C/ Numerical Recipes in C++/Numerical Recipes in Fortran/ NUmerical Methods in Matlab
 
Dr Transport, PerennialII, neurocomp2003,

Thanks for your suggestions.

Keep the recommendations coming...

Any 'classics' come to mind (like Schlichting is to Boundary Layer Theory, Zienkiewicz is to the Finite Element Method, Timoshenko is to Theory of Plates and Shells, Knuth is to Computer Algorithms, Kernighan and Ritchie are to the C Programming Language, etc.)? :-p
 
I know I'm almost two months late, but I can't resist a question about numerical method books!

For optimization, the best book I have seen is free right here
http://www.stanford.edu/~boyd/cvxbook/
Lots of examples in there.

For numerical methods, I have never seen a good book on solving ODEs and stuff like FEM, but a wonderful book on the important smaller numerical techniques (like system solving and SVD) is
http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/text.html
That book is very readable, and presents things in a very intuitive manner. Definitely the best book I have seen on the subject.

One other thing I have encountered that I thought gave very intuitive explanations is
http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf
It basically explains how iterative system solvers work, and has lots of pictures to help explain things.
 
Last edited by a moderator:

Similar threads

  • · Replies 18 ·
Replies
18
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 8 ·
Replies
8
Views
1K
  • · Replies 5 ·
Replies
5
Views
5K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
28
Views
5K
  • · Replies 5 ·
Replies
5
Views
5K
Replies
2
Views
8K