Introduction to Applied Numerical Analysis
This book covers an extensive range of topics, including round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogonal functions, and Fourier series. 1989 edition.
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accuracy algebra approximation arithmetic basic binary bisection method calculation Chap Chebyshev approximation Chebyshev polynomials coefficients column complex zeros computing constraints decimal derivative determinant differential equation digits edition equally spaced error term estimate evaluation exactly examine example expansion false-position method finite floating point formula Fourier series function f(x function values Gaussian elimination geometry given hence idea imaginary curves integration interpolation interval least-squares Legendre polynomials library routine linear machine mathematical matrix minimize minimum multiple zero negative gradient Newton's method number system numerical analysis objective function optimization orthogonal functions orthogonal polynomials parameters pivoting plane point number polynomial of degree practice probably problem quadrant numbers quadratic factors random numbers real zeros reasonable result roundoff error sample points scaling sequence sign changes simple solution solve square step Taylor series theorem theory tion trapezoid rule truncation error usually variable