·280· 附录C高性能计算-科学计算软件介绍 ·NTEGRATION -Golub Welsch (1969)Gauss quadrature rules -de Boor(1971)adaptive quadrature algorithms ·APPROXIMATION -Remes(1934)Remes algorithm for Chebyshev approx. -Schoenberg (1946)splines -Powell(1967)near-optimality of Chebyshev interp. -Reinsch(1967)smoothing with splines -Cox(1972)calculation with B-splines -de Boor(1972)calculation with B-splines ·OTHER -Aitken(193)Aitken extrapolation -Cooley Tukey (1965)the fast Fourier transform -Greengard&Rokhlin (1987)fast multipole methods ODEs -Curtiss Hirschfelder(1952)stiffness and BD formulas -Dahlquist (156)stability and convergence -Dahlquist(1963)A-stability -Butcher(1965)Runge-Kutta methods Gear(1969)stiff ODEs -Wanner,Hairer Norsett(1978)order stars and stability theorems ·ELLIPTIC PDEs -Peaceman Rachford (1955)ADI Douglas(1955)ADI -Strang(1971 or 1973)finite elements and approx.theory -Buzbee,Golub&Nielsen(1970)fast Poisson via cyclic reduction -Hockney(1965)fast Poisson via FFT -Fedorenko(1961)multigrid methods -Brandt(1977)multigrid methods PARABOLIC AND HYPERBOLIC PDEs -Courant,Friedrichs&Lewy (1928)the CFL condition -Crank Nicolson (1947)finite differences for parabolic PDE O'Brien,Hyman Kaplan(1951)Von Neumann stability analysis -Lax&Richtmyer(196)general stability theory -Lax Wendroff (1960,1962,1964)methods for solving conservation laws -Kreiss(1962)more general stability theory -Orszag (1971)spectral methods -Kreiss Oliger(1972)spectral methods· 280 · 附录 C 高性能计算 – 科学计算软件介绍 • INTEGRATION – Golub & Welsch (1969) Gauss quadrature rules – de Boor (1971) adaptive quadrature algorithms • APPROXIMATION – Remes (1934) Remes algorithm for Chebyshev approx. – Schoenberg (1946) splines – Powell (1967) near-optimality of Chebyshev interp. – Reinsch (1967) smoothing with splines – Cox (1972) calculation with B-splines – de Boor (1972) calculation with B-splines • OTHER – Aitken (1932) Aitken extrapolation – Cooley & Tukey (1965) the fast Fourier transform – Greengard & Rokhlin (1987) fast multipole methods • ODEs – Curtiss & Hirschfelder (1952) stiffness and BD formulas – Dahlquist (1956) stability and convergence – Dahlquist (1963) A-stability – Butcher (1965) Runge-Kutta methods – Gear (1969) stiff ODEs – Wanner, Hairer & Norsett (1978) order stars and stability theorems • ELLIPTIC PDEs – Peaceman & Rachford (1955) ADI – Douglas (1955) ADI – Strang (1971 or 1973) finite elements and approx. theory – Buzbee, Golub & Nielsen (1970) fast Poisson via cyclic reduction – Hockney (1965) fast Poisson via FFT – Fedorenko (1961) multigrid methods – Brandt (1977) multigrid methods • PARABOLIC AND HYPERBOLIC PDEs – Courant, Friedrichs & Lewy (1928) the CFL condition – Crank & Nicolson (1947) finite differences for parabolic PDE – O’Brien, Hyman & Kaplan (1951) Von Neumann stability analysis – Lax & Richtmyer (1956) general stability theory – Lax & Wendroff (1960,1962,1964) methods for solving conservation laws – Kreiss (1962) more general stability theory – Orszag (1971) spectral methods – Kreiss & Oliger (1972) spectral methods