Tractability of tensor product linear operators in weighted Hilbert spaces.
Information and Computation
The paper is an exposition of the information-centered approach to problems that are solved with uncertainty. The theory and application of the information-centered is called -complexity. The authors have introduced the basic quanities and fundamental invariant which they call the radius of information and which tells how well a problem can be solved. They present this quantities and contrast the informationcentered approach with the algorithm-centered approach.
The inverse of the star-discrepancy depends linearly on the dimension
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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