### Basic concepts in numerical error analysis (suggested by linear algebra problems)

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It is shown that iterative refinement (using normal equations and exclusively standard floating point arithmetic with relative precision v) yields almost full accuracy of computed solution to regular linear least squares problem, provided some conditions.

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.

The various approaches to estimation of the numerical methods errors are discussed.

It is shown that each quadrature computed by Romberg algorithm is exact for slightly perturbed data (computed values of the integrand). For the ordinary summation algorithm the cumulation of rounding errors is proportional to N, the number of quadrature modes. For more elaborate summation the cumulation is proportional to log N. For the binary floating point arithmetic with proper rounding of the sum, the cumulation of errors can be made practically independent of N. In each case the influence of...

In the paper the problem of solution for the system of the linear equations with sparse matrix is considered.

The article contains no abstract

In the paper an analysis of errors of the solution of system of the nonsingular linear equations is given. The numerically stable algorithm, implemented in the floating point arithmetics available in modern computers, is applied.

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