Rounding error analysis of the classical Gram-Schmidt orthogonalization process
نویسندگان
چکیده
1 CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France ([email protected]). 2 The University of Tennessee, Department of Computer Science, 1122 Volunteer Blvd., Knoxville, TN 37996-3450, USA ([email protected]). 3 Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věž́ı 2, CZ-182 07 Prague 8, Czech Republic ([email protected]). 4 Heinrich-Heine-Universität, Mathematisches Institut, Universitätsstrasse 1, D-40225 Düsseldorf, Germany ([email protected]).
منابع مشابه
The Loss of Orthogonal i ty in the Gram - Schmidt Orthogonal izat ion Process
K e y w o r d s N u m e r i c a l linear algebra, QR factorization, Gram-Schmidt orthogonalization, Reorthogonalization, Rounding error analysis. 1. I N T R O D U C T I O N Scientific comput ing and ma themat i ca l models in engineering are becoming increasingly dependent upon development and implementa t ion of efficient paral le l a lgor i thms on modern high performance computers . Numerica...
متن کاملA Robust Criterion for the Modified Gram-Schmidt Algorithm with Selective Reorthogonalization
A new criterion for selective reorthogonalization in the modified Gram–Schmidt algorithm is proposed. We study its behavior in the presence of rounding errors. We give some counterexample matrices which prove that the standard criteria might fail. Through numerical experiments, we illustrate that our new criterion seems to be suitable also for the classical Gram– Schmidt algorithm with selectiv...
متن کاملA New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel Method
This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The conver...
متن کاملA new reproducing kernel method for solving Volterra integro-dierential equations
This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the...
متن کاملFPGA-based Normalization for Modified Gram-Schmidt Orthogonalization
Eigen values evaluation is an integral but computation-intensive part for many image and signal processing applications. Modified Gram-Schmidt Orthogonalization (MGSO) is an efficient method for evaluating the Eigen values in face recognition algorithms. MGSO applies normalization of vectors in its iterative orthogonal process and its accuracy depends on the accuracy of normalization. Using sof...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Numerische Mathematik
دوره 101 شماره
صفحات -
تاریخ انتشار 2005