Описание: Since this is a 2nd Edition, we are giving below the topics we wish to add/update/revise in roughly the same chapter sequence as we had in the existing 1st Edition of the book. In addition to a general revision of the text, we propose the following major modifications (the asterisks denote the amount of text added/modified and/or or the difficulty level of the topics being discussed):
Chapter 2
- Subsection 2.1.2: add discussion on how to find all zeros by means
of the Newton method (*)
Chapter 3
- Expand Subsection 3.2.7 on solving the A*x = b equations with sparse
matrices to a full Section (**)
- Expand Subsection 3.4.5 on solving the eigenvalue problem A*x = lambda*x
to a full Section (**) - Discuss the exponentiation of a matrix, exp(A) (*)
- Add a Subsection on Pseudospectra (**)
- in general
, enhance the sparse aspect of the chapter
Chapter 4
- Add a new Section on Sparse FFT (following present Sec. 4.2),
add corresponding Exercise (**)
- Expand Subsection 4.6.2 on the Discrete Wavelet Transform
to a full Section, add Exercise (***)
- Add a Section on image denoising (**)
- Add Section on Radon transformation (**)
Chapter 5
- Rewrite Sections 5.1-5.5 to better distinguish between general
discussion of distributions and the techniques involving samples,
and to bring the notation in line with the book Probability
for Physicists (***)
- Introduce Bayesian data analysis and inference (***)
- Expand Subsection 5.5.8 on Non-linear Regression to a full Section,
add Exercises (**)
Chapter 6
- Expand Section 6.5
on Noise, add Exercise (**) - Add Section on Takens Theorem and its applications: phase space
reconstruction and optimal size determination (**) - Add discussion on signal entropies (**)
- Update discussion on autoregressive models (optimal order) (*)
- Add discussion on signal directionality / causality (**)
Chapter 7
- Expand Section 7.10 on Stiff Problems of ODE, add Exercise (**)
Chapter 8
- Expand Subsection 8.7.4 on Singular SL Problems to a Section,
add Exercise (**)
- Motivated by Section 8.8, write a new chapter on Inverse Problems (***)
Chapter 10
- Expand Section 10.8, add Exercise (**)
Chapter 11
- Expand Sections 11.7 and 11.8, add Exercises (**)
New Chapter on Inverse Methods (***)
New short Chapter or Appendix on minimization (**)
- with derivatives or without them
- with constraints or without them
- deterministic and quasi-deterministic (MC methods)
New Appendix on spline methods: B-splines, Bezier splines (**)
