Table 1.Some past and future developments in scientific computing.The asterisks mark items summarised by (*) Before 1940 Newton's method Gaussian elimination Gauss quadr ature least-squares fitting Adams and Runge-Kutta formulas Richardson extrapol ation 1940-1970 floating point arithmetic Fortran finite differences finite elements simplex algorithm Monte Carlo orthogonal linear algebr a splines FFT 1970-2000 quasi-Newton iterations adaptivity stiff ODE solvers software libr aries Matlab multigrid spar se and iterative line ar algebra spectral methods interior point metho ds wavelet s 2000-2048 linear algebra in O(N2+)flops multipole methods breakthroughs in preconditioners,spectral methods,time stepping for PDE speech and graphics every where fully intelligent,adaptive numerics loss of determinism seamless interoperability massively par allel computing made possible by ideas related to the human brain new programming methods made possible by ideas related to natur al selection 8Table  Some past and future developments in scientic computing The asterisks mark items summarised by  Before  Newton s method Gaussian elimination Gauss quadrature least squares tting Adams and Runge Kutta formulas Richardson extrapolation   oating point arithmetic Fortran nite dierences nite elements simplex algorithm Monte Carlo orthogonal linear algebra splines FFT   quasi Newton iterations adaptivity sti ODE solvers software libraries Matlab multigrid sparse and iterative linear algebra spectral methods interior point methods wavelets    linear algebra in ON￾￾  ops multipole methods breakthroughs in preconditioners spectral methods time stepping for PDE  speech and graphics everywhere  fully intelligent adaptive numerics  loss of determinism  seamless interoperability  massively parallel computing made possible by ideas related to the human brain  new programming methods made possible by ideas related to natural selection