Titlebook: Condition; The Geometry of Nume Peter Bürgisser,Felipe Cucker Book 2013 Springer-Verlag Berlin Heidelberg 2013 complexity.condition numbers

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acquisition

The Linear Programming Feasibility Problemn interior-point method to the latter and obtain an algorithm solving . with a complexity bounded by a low-degree polynomial in .,. and .. A question conspicuously left open is the solution of the optimization problem itself. The main theorem of Chap. . provides a key step of this solution but leave

乞丐

Condition and Linear Programming Optimizationroblems in standard form, . and . If such an algorithm decides that a triple . is feasible, we may want to compute the optimizers .. and .., as well as the optimal value .., of the pair (SP)–(SD). To do so is the goal of this chapter..An approach to this problem is to apply the interior-point algori

Platelet

hemoglobin

Probabilistic Analyses of the GCC Condition Numberater on, we saw that this quantity occurs in cost estimates for an ellipsoid method finding feasible points in a nonempty cone and for interior-point methods deciding feasibility of polyhedral conic systems. Furthermore, the development in Chap. . showed that this condition number also plays a centr

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OTTER

Using the Web to Process Transactions number for linear equation solving, . where .(.) is defined with respect to the spectral norm and .(.) with respect to the Euclidean norm. Inequality (*) calls for a deeper understanding of what .(.,.) is than the equality above. The pursuit of this understanding is the goal of this chapter.

平淡而无味

教唆

Using the Web to Process Transactions matrices are, in general, ill-conditioned. We prove that if . is a lower-triangular matrix whose entries are independent standard Gaussian random variables, then .. This yields an expected loss of precision satisfying . Were the loss of precision in the solution of triangular systems to conform to

最小

The Challenge Posed by Long Transactionse bounds obtained are independent of . and depend only on the upper bound on the elongation ./.. Furthermore, surprisingly, they are also independent of ...These results indicate that for large reasonably elongated matrices, one may expect the loss of precision in the solution of least-squares probl