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Numerical stability in problems of linear algebra.Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.
Document ID
19720042195
Document Type
Reprint (Version printed in journal)
Authors
Babuska, I. (Maryland, University College Park, Md., United States)
Date Acquired
August 6, 2013
Publication Date
March 1, 1972
Publication Information
Publication: SIAM Journal on Numerical Analysis
Volume: 9
Subject Category
MATHEMATICS
Funding Number(s)
CONTRACT_GRANT: AT(40-1)-3443
CONTRACT_GRANT: NGL-21-002-008
CONTRACT_GRANT: NSF GU-2061
Distribution Limits
Public
Copyright
Other