TAILIEUCHUNG - Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 88

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 88', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 98 Chapter2. Solution ofLinearAlgebraic Equations x i sum p i A typical use of choldc and cholsl is in the inversion of covariance matrices describing the fit of data to a model see . . In this and many other applications one often needs L-1. The lower triangle of this matrix can be efficiently found from the output of choldc for i 1 i n i a i i p i for j i 1 j n j sum for k i k j k sum - a j k a k i a j i sum p j CITED REFERENCES AND FURTHER READING Wilkinson . and Reinsch C. 1971 Linear Algebra vol. II of Handbook for Automatic Computation New York Springer-Verlag Chapter I 1. Gill . Murray W. and Wright . 1991 Numerical Linear Algebra and Optimization vol. 1 Redwood City CA Addison-Wesley . Dahlquist G. and Bjorck A. 1974 Numerical Methods Englewood Cliffs NJ Prentice-Hall . Golub . and Van Loan . 1989 Matrix Computations 2nd ed. Baltimore Johns Hopkins University Press . QR Decomposition There is another matrix factorization that is sometimes very useful the so-called QR decomposition A Q R Here R is upper triangular while Q is orthogonal that is Qt Q 1 where QT is the transpose matrix of Q. Although the decomposition exists for a general rectangular matrix we shall restrict our treatment to the case when all the matrices are square with dimensions N x N. Like the other matrix factorizations we have met LU SVD Cholesky QR decomposition can be used to solve systems of linear equations. To solve A x b Sample page from NUMERICAL RECIPES IN C THE ART OF SCIENTIFIC COMPUTING ISBN 0-521-43108-5 first form QT b and then solve R x Qt b by backsubstitution. Since QR decomposition involves about twice as many operations as LU decomposition it is not used for typical systems of linear equations. However we will meet special cases where QR is the method of choice. QR Decomposition 99 The standard algorithm for the QR decomposition involves successive Householder transformations to be discussed

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