Acta Numerica 1999: Volume 8Arieh Iserles Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing. |
Contents
We describe the burgeoning field of numerical relativity which aims to solve | 2 |
Initial data | 14 |
Evolution | 25 |
Related literature | 38 |
Radiation boundary conditions for the numerical | 47 |
Numerical methods in tomography | 107 |
Approximation theory of the MLP model in neural networks | 143 |
An introduction to numerical methods for stochastic | 197 |
Computation of pseudospectra | 247 |
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Common terms and phrases
a(Yn Acta Numerica activation function Anal apparent horizon Appl applications approximation b(Yn black hole coefficients Comput constraint construction convergence convolution dense in C(R density derivatives discrete domain eigenvalues Einstein's equations error estimates Euler Euler approximation evolution exact boundary conditions exact conditions formula Fourier transform gravitational grid Hagstrom hidden layer model hyperbolic IEEE Trans initial data integrals interpolation inversion iteration Itô Kloeden and Platen linear lower bound Math mathematical matrix metric Monte Carlo Methods neural networks nonlinear norm numerical analysis numerical methods numerical schemes numerical solution operator Padé approximants perceptron Phys planar polynomial problem pseudospectra Radon transform random reconstruction result ridge functions SDEs Section SIAM sigmoidal sigmoidal function simulation solution of stochastic solving spacetime spherical Springer step-size stochastic differential equations Stratonovich subspace Talay techniques tensor Theorem theory tions tomography Trefethen variables vector wave equation weak Wiener process Yn+1 ди