Concise Numerical Mathematics
This book succinctly covers the key topics of numerical methods. While it is basically a survey of the subject, it has enough depth for the student to walk away with the ability to implement the methods by writing computer programs or by applying them to problems in physics or engineering. The author manages to cover the essentials while avoiding redundancies and using well-chosen examples and exercises. The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for many algorithms, which can be easily converted to computer programs. Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.In general, the author assumes only a knowledge of calculus and linear algebra. The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science.
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arbitrary arithmetic operations Arnoldi process boundary value problem calculation coefficients completes the proof consider consistency order constant convergence Corollary corresponding cubic spline denotes determined discrete Fourier transform eigenvalues entries error estimate error representation example Exercise factorization fc=i Figure floating point number following holds following theorem follows directly function f G RN Galerkin method Hessenberg Hessenberg matrix identity inequality initial value problem interpolating polynomial interpolation interval introduced iteration error iteration function Jacobi method Lemma linear subspace linear system Lipschitz condition m-step method matrix A G RN*N matrix norm multistep methods Newton's method notation obtains one-step method orthogonal pairwise distinct point number system positive definite proof of Theorem QR algorithm regular matrix Remark respect satisfied scalar product Section solution statement support abscissas symmetric symmetric matrix system F system of equations upper triangular vector norm yields