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In a finite-dimensional real or complex linear normed space X there are characterized all the sets of operators A1,...,An which sum up to the identity operator and such that ||Aix||+...+||Anx|=||x|| for all xX. An example of application in the theory of stability of difference schemes is given.
Part I contains rounding-error analysis of Gaussian elimination for the triangular factorization and for solving linear systems in the case of tridiag-onal symmetric definite matrix.
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