Elementary Theory & Application of Numerical Analysis
Courier Corporation, 2011 - Mathematics - 315 pages
This updated introduction to modern numerical analysis is a complete revision of a classic text originally written in Fortran but now featuring the programming language C++. It considers a relatively small number of basic concepts and techniques, focusing on how and why each method works. The authors offer careful consideration of error-analysis aspects related to the problems and algorithms.
The treatment also reviews and solidifies basic concepts from elementary calculus, emphasizing theory and proofs. It makes repeated use of the mean-value theorem, intermediate-value theorem, and Taylor's series. Many exercises appear throughout the text, most with solutions, and an extensive tutorial explains how to solve problems with C++.
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Elementary Theory and Application of Numerical Analysis
David G. Moursund,Charles S. Duris
Limited preview - 1988
algorithm Algorithm 3-1 Apply approximate value ax ax calculation chapter coefficients continuous convergence cout deﬁned derivatives diagonal differential equations discussed elements endl error bound Euler’s method evaluation exact solution example exerCise 28 exists ﬁnd ﬁrst ﬁrst-order fixed-point iteration floating-point arithmetic for(i formula forrn function f(x given gives Hence Heun’s method Hilbert matrix inherent error Input int main integration interval linear equations linear interpolation linear system Lipschitz condition loop mantissa matrix Newton-Raphson iteration notation numerical analysis numerical differentiation output polynomial problem procedure proof Prove remainder result Richardson’s extrapolation round-off error Runge-Kutta Runge-Kutta method satisﬁes satisfies a Lipschitz sequence Simpson’s rule solve Suppose systemAX Taylor’s series theorem tion trapezoidal rule truncation error unique solution variable Write a program zero ε ε