Numerical Methods in Scientific Computing: Volume 1
This new book from the authors of the classic book Numerical methods addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines traditional and well-developed topics with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLAB multiple precision package; and a guide to literature, algorithms, and software in numerical analysis. Review questions, problems, and computer exercises are also included. For use in an introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.
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accuracy algebraic algorithm analysis analytic applied arithmetic asymptotic B-splines Chebyshev Cited coefﬁcients complex computed continued fraction convergence convergence acceleration curve decimal deﬁned deﬁnition derivatives determined difference equation differential equations digits double precision efﬁcient equidistant error bound error estimate Euler evaluated exact example expansion ﬁnd ﬁnite ﬁrst ﬁxed ﬂoating-point formal power series Fourier function f function values Gaussian elimination given gives grid Hence IEEE inﬁnite integral interpolation formula interval iteration linear system mathematical MATLAB matrix modiﬁed Monte Carlo method multiplication Newton’s method nodes notation Note obtained operations orthogonal polynomials Padé approximants points polynomial of degree problem Proof quadratic quadrature rules random numbers recurrence relation remainder result Richardson extrapolation root rounding errors satisﬁes secant method sequence Show solution solving spline step sufﬁciently Theorem Toeplitz matrix transformation trapezoidal rule triangular truncation error variable vector xn+1 zero