Introduction to numerical analysis
Author Alastair Wood provides a clear and concise book for novice numerical analysts. Computer based experiments allow readers to learn by doing. Methods are developed with sufficient background, allowing readers to see why a method works and when a method does not work. Wood offers an introduction to the more basic theoretical elements, as well as generating practical skills. Computer skills and real applications are stressed as Wood explores such topics as the Taylor Series, Maclaurin Series, Jacobi Iteration and Gauss-Seidel iteration. For novice Numerical Analysts.
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A-stable absolute error accuracy Algebra algorithm applied approA approximation arithmetic Author behaviour bisection method Blot calculations coefﬁcients column constant convergence cubic decimal places deﬁned deﬁnition DERIVE Experiment difference equation differential difﬁcult divided difference equal equispaced error analysis error bound estimate Euler Euler’s method evaluate Example expression f x0 Figure ﬁnal ﬁnd ﬁnding ﬁrst ﬁrst-order ﬁxed point ﬂoating-point ﬂops formula forward elimination function f function values Gauss—Seidel gives graph implement implify integration interpolating polynomial interval least-squares linear logistic mapping Maclaurin series mathematician mathematics matrix modiﬁed Newton Newton—Raphson nodes numerical methods numerical solution obtained Padé Padé approximants pivot point x0 quadratic rectangle rules recurrence relation reﬁned relative error result retums Riemann Riemann sum root rounding error Runge—Kutta method satisﬁes second-order Section slope solve speciﬁed spline step size h sub-intervals sufﬁciently Taylor polynomial Taylor series trapezium rule truncation error zero