A First Course in Numerical Analysis
Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems -- some strictly mathematical, others requiring a computer -- appear at the end of each chapter.
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CHAPTER ONE INTRODUCTION
CHAPTER TWO APPROXIMATION
18 other sections not shown
abscissas accuracy algorithm arithmetic assume bound calculate Chap Chebyshev polynomials coefficients column consider convergence corrector corresponding deduce defined derive determine diagonal difference digital computer discussed eigenvalues eigenvectors elements error term estimate evaluate example extrapolation floating-point follows Gaussian elimination given initial approximation interval inverse iterative methods least-squares approximation linear magnitude Math matrix maximum error multiplications Newton-Cotes Newton-Cotes formulas Newton-Raphson method Newton's method norm notation Note numerical analysis numerical integration method numerical solution Ordinary Differential Equations orthogonal polynomials Pade approximations polynomial of degree predictor problem quadrature formula rational function relative error results of Prob right-hand side root roundoff error Runge-Kutta methods satisfies secant method sequence solve spline stability step subintervals tabular points technique theorem tion trapezoidal rule triangular true value truncation error variable vector weight function zero