Basic concepts in numerical error analysis (suggested by linear algebra problems)
The summation algorithm with correction and their applications
Review: M. Kolupa, J. M. Witkowski,Selected numeic methodes of linear algebra in econometrics
The article contains no abstract
Iterative refinement of least squares solutions computed from normal equations
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.
Stability of the Gaussian elimination for special classes of matrices. Part I
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.
Error estimation in elimination method
The various approaches to estimation of the numerical methods errors are discussed.
Rounding Errors in Romberg Algorithm
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...
Algorithm of the best strategy method for hugh systems of the linear equations with symmetric, positively definite matrices
In the paper the problem of solution for the system of the linear equations with sparse matrix is considered.
To readers, authors, referees, formal and informal co-workers of Matematyka Stosowana-Applied Mathematics
The article contains no abstract
Estimation of error for the solution of system of linear equations and application of the improved summation in algorithms of the linear algebra
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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