文档介绍：Nick Trefethen
puting Lab
Who invented the great numerical algorithms?
Slides available at my web site:
.uk/
A discussion over coffee.
Ivory tower or coal face?
SOME MAJOR DEVELOPMENTS IN PUTING
(29 of them)
Before 1940
Newton's method
least-squares fitting orthogonal linear algebra
Gaussian elimination QR algorithm
Gauss quadrature Fast Fourier Transform
Adams formulae quasi-Newton iterations
Runge-Kutta formulae
finite differences 1970-2000
preconditioning
1940-1970 spectral methods
floating-point arithmetic MATLAB
splines multigrid methods
Monte Carlo methods IEEE arithmetic
simplex algorithm nonsymmetric Krylov iterations
conjugate gradients & Lanczos interior point methods
Fortran fast multipole methods
stiff ODE solvers wavelets
finite elements automatic differentiation
Before 1940
Newton’s Method for nonlinear eqs.
Heron, al-Tusi 12c, Al Kashi 15c, Viète 1600, Briggs 1633…
Isaac Newton 1642-1727
Mathematician and physicist
Trinity College, Cambridge, 1661-1696
(BA 1665, Fellow 1667,
Lucasian Professor of Mathematics 1669)
De analysi per aequationes numero terminorum infinitas 1669 (published 1711)
After 1696, Master of the Mint
Joseph Raphson 1648-1715
Mathematician at Jesus College, Cambridge
Analysis Aequationum universalis 1690
Raphson’s formulation was better than Newton’s (“plus simple”- Lagrange 1798)
FRS 1691, . 1692
Supporter of Newton in the calculus wars—History of Fluxions, 1715
Thomas Simpson 1710-1761
1740: Essays on Several Curious and Useful Subjects…
1743-1761: Royal Military Academy, Woolwich
Important!—first to treat non-polynomial equations, first to treat systems of eqs.
Least-squares fitting
Carl Friedrich Gauss 1777-1855
Mathematics, astronomy, geodesy, ism
1792-1795: Braunschweig Collegium Carolinum
1795, but not published until 1809
(→ big fight with Legendre)
(During this time as a teenager in Braunschweig he also discovered the
binomi