Journal of Computational Physics
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
Journal of Approximation Theory
Parallel adaptive time domain decomposition for stiff systems of ODEs/DAEs
Computers and Structures
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Parameter estimation and accuracy matching strategies for 2-D reactor models
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Applying numerical continuation to the parameter dependence of solutions of the Schrödinger equation
Journal of Computational and Applied Mathematics
Local convergence of Newton's method under majorant condition
Journal of Computational and Applied Mathematics
A Finite Element Method for Density Estimation with Gaussian Process Priors
SIAM Journal on Numerical Analysis
Original article: A quantitative metric for robustness of nonlinear algebraic equation solvers
Mathematics and Computers in Simulation
An efficient and general numerical method to compute steady uniform vortices
Journal of Computational Physics
A minimal norm corrected underdetermined Gauß-Newton procedure
Applied Numerical Mathematics
Using the fisher-rao metric to compute facial similarity
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
Journal of Computational Physics
Automatic Fréchet Differentiation for the Numerical Solution of Boundary-Value Problems
ACM Transactions on Mathematical Software (TOMS)
On the Finite Element Approximation of $p$-Stokes Systems
SIAM Journal on Numerical Analysis
Polynomial chaos for boundary value problems of dynamical systems
Applied Numerical Mathematics
Large-scale Tikhonov regularization of total least squares
Journal of Computational and Applied Mathematics
Secant-type methods and nondiscrete induction
Numerical Algorithms
Advances in Engineering Software
New quasi-Newton iterative learning control scheme based on rank-one update for nonlinear systems
The Journal of Supercomputing
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This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.