Scientific Computing: An Introductory SurveyMcGraw-Hill, 2002 - 563 pagine Scientific Computing, 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinearequations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems.Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization.The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems. |
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Risultati 1-3 di 30
Pagina 183
... QR iteration in effect produces QR factorizations of successive pow- ers of A , and hence the columns of Qk form an orthonormal basis for the subspace spanned by the columns of A * , which in turn result from applying simultaneous ...
... QR iteration in effect produces QR factorizations of successive pow- ers of A , and hence the columns of Qk form an orthonormal basis for the subspace spanned by the columns of A * , which in turn result from applying simultaneous ...
Pagina 184
... QR iteration to produce a highly efficient algorithm for computing all the eigenvalues and corresponding eigenvectors of any matrix . As with any variant of power iteration , the convergence rate of QR iteration depends on the ratio of ...
... QR iteration to produce a highly efficient algorithm for computing all the eigenvalues and corresponding eigenvectors of any matrix . As with any variant of power iteration , the convergence rate of QR iteration depends on the ratio of ...
Pagina 187
... iteration . As we saw in Chapter 3 , the QR factorization of a general n x n matrix that must be performed for each QR iteration requires O ( n3 ) work . This work could be substantially reduced , however , if the matrix were already ...
... iteration . As we saw in Chapter 3 , the QR factorization of a general n x n matrix that must be performed for each QR iteration requires O ( n3 ) work . This work could be substantially reduced , however , if the matrix were already ...
Sommario
Scientific Computing | 1 |
Initial Value Problems for ODEs | 9 |
Systems of Linear Equations | 49 |
Copyright | |
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Scientific Computing: An Introductory Survey, Revised Second Edition Michael T. Heath Anteprima limitata - 2018 |
Scientific Computing: An Introductory Survey, Revised Second Edition Michael T. Heath Anteprima limitata - 2018 |
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accuracy algorithm approximate solution basis functions Cholesky factorization coefficients column complex components compute condition number constraints convergence rate corresponding data points defined derivative determine differential digits dimension eigenvalues eigenvectors Euler's method evaluate Example finite difference floating-point number floating-point system function f function values Gaussian elimination given golden section search gradient hence Hessian matrix Householder transformation implementation initial input integral integrand interval inverse inverse iteration iterative method Lagrange least squares problem library routine linear equations linear least squares linear system LU factorization MATLAB method for solving minimizing multiple n x n Newton's method nonlinear equations nonsingular nonzero norm objective function obtain one-dimensional optimization problem orthogonal parameters perturbations pivoting polynomial interpolation positive definite programming QR factorization QR iteration quadratic quadrature rule relative residual resulting root scalar secant method Section sequence singular value spline symmetric tion tridiagonal True or false upper triangular vector zero