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An Overview of Numerical
Computer Number Representation and Roundoff
Simultaneous Linear Equations
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accuracy algorithm Application arithmetic ARRAY bisection bisection method calculation CALL SEQUENCE Chapter coefficients computed solution CONTINUE convergent data points decimal defined denote derived system diagonal differential equation digits DIMENSION discrete Fourier transform double precision eigenvalue ENDPOINT error bound estimate Euler's method evaluate EXAMPLE Figure floating-point formula function f(x function values Gauss quadrature Gaussian elimination Horner's rule illustrated initial INPUT integral integrand interpolating points interpolation polynomial interpolatory quadrature interval inverse iterations least-squares polynomial linear equations machine epsilon matrix Newton-Cotes Newton's method nonlinear equations obtained orthogonal OUTPUT parameters partial pivoting piecewise polynomial approximation Problem quadratic quadrature points recursive representation RETURN END Romberg Romberg integration root roundoff error Runge-Kutta method satisfy secant method Section Simpson's rule solving step size h STOP END subintervals SUBROUTINE SUBROUTINE COMPUTES Taylor's polynomial Taylor's series techniques trapezoidal rule truncation error variables vector zero