Elementary Numerical Computing with Mathematica
Robert D. Skeel, Jerry B. Keiper · CERN Document Server (European Organization for Nuclear Research) · 1993
Applications computational errors algorithms error error propagation floating-point computation positional number systems floating-point numbers rounding basic operations numerical instability other difficulties rootfinding roots bisection method Newton's method functional interaction secant method systems of linear equations matrices norms and sensitivity Gaussian elimination accuracy of partial pivoting linear equation solvers large sparse systems LU factorization interpolation Taylor's series big-oh notation existence and uniqueness Lagrange form inverse interpolation least squares approximation the least squares problem orthogonality the normal equations numerical differentiation and integration numerical differentiation simple quadrature rates Gaussian quadrature rules numerical error estimates global adaptive quadrature ordinary differential equators a single ODE Euler's method systems of ODE's Taylor series methods Runge-Kutta methods overview. Appendices: Getting started with Mathematica exact and approximate numerical calculations algebraic calculations lists defining functions procedural programming expressions defining rules how evaluation works delayed evaluation.