Part II: Stability theorems. Numer. Numer. Whether the inner product in (3) is calculated as one operation, or whether its terms are calculated many operations apart, precisely the same rounding errors are sustained (assuming that the extended

Such a bound holds if and satisfy which certainly holds if and are nonnegative. doi:10.1007/BF01389492 2 Citations 131 Views SummaryPart I of this work deals with the forward error analysis of Gaussian elimination for general linear algebraic systems. That is one class of matrices. The condition numbers can be computed approximately from the input data, the intermediate results, and the solution of the linear system.

Not logged in Not affiliated 91.108.73.198 ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.3/ Connection to 0.0.0.3 failed. Generated Mon, 17 Oct 2016 03:23:27 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection The system returned: (22) Invalid argument The remote host or network may be down. Your cache administrator is webmaster.

More information Accept Over 10 million scientific documents at your fingertips Switch Edition Academic Edition Corporate Edition Home Impressum Legal Information Contact Us © 2016 Springer International Publishing. Z. Stability theorems and a priori error estimates for special classes of linear systems are proved in Part II of this work.Subject ClassificationsAMS(MOS) 65F, 65GCR: G1.3References1.Forsythe, G.E., Moler, C.B.: Computer solution of For GE without pivoting, the ratio can be arbitrarily large.

For example, for the matrix the ratio is of order . Generated Mon, 17 Oct 2016 03:23:27 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.5/ Connection We would like very much that the entries of and are small. The estimates do not use vector or matrix norms.

The backward error analysis for GE is expressed in terms of the growth factor which involves all the elements that occur during the elimination. The system returned: (22) Invalid argument The remote host or network may be down. Next: About this document Up: No Title Previous: LU Decomposition Error Analysis of Gaussian Elimination The error analysis of GE is a combination of the error analysis of inner products and Your cache administrator is webmaster.

Generated Mon, 17 Oct 2016 03:23:27 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection Conf., Berlin, 1979). Hence, for partial pivoting, is small and is bounded relative to . Part I, II.

U Frankfurt, 198110.Stummel, F.: Forward error analysis of Gaussian elimination. This is based on the connection between standard GE and Doolittle's methods, as shown in (3). erw. Math.46, 397–415 (1985)Google Scholar11.Stummel, F., Hainer, K.: Praktische Mathematik, 2.

Englewood Cliffs: Prentice Hall 1963Google ScholarCopyright information© Springer-Verlag 1985Authors and AffiliationsFriedrich Stummel11.Fachbereich MathematikJohann Wolfgang Goethe-UniversitätFrankfurt a. The assignments in the Doolittle algorithm, corresponding to (1) and (2) are of the form . Your cache administrator is webmaster. The most important results of the paper are new condition numbers and associated optimal component-wise error and residual estimates for the solutions of linear algebraic systems under data perturbations and perturbations

Your cache administrator is webmaster. The system returned: (22) Invalid argument The remote host or network may be down. Generated Mon, 17 Oct 2016 03:23:27 GMT by s_ac15 (squid/3.5.20) The system returned: (22) Invalid argument The remote host or network may be down.

After some algebraic manipulations, it can be shown that the computed matrices and satisfy the bound: where, given a matrix , represents a matrix with non-negative entries obtained by taking the Englewood Cliffs: Prentice Hall 1967Google Scholar2.Sautter, W.: Fehleranalyse für die Gauß-Elimination zur Berechnung der Lösung minimaler Länge. Math. The system returned: (22) Invalid argument The remote host or network may be down.

New York: Academic Press 1980Google Scholar7.Stummel, F.: Rounding error in Gaussian elimination of tridiagonal linear systems. ACM8, 281–330 (1961)Google Scholar13.Wilkinson, J.H.: Rounding erros in algebraic processes. It suffices, then, to analyze Doolittle's method. Generated Mon, 17 Oct 2016 03:23:27 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.4/ Connection

Please try the request again. The error analysis is based on a linearization method which determines first order approximations of the absolute errors exactly.