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

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Using the Web to Process Transactionsst invariably, the use of .(.) is enough to provide a satisfying explanation of the phenomena observed in practice..The case of triangular systems of linear equations provides, in contrast, an example in which .(.) turns out to be inadequate. Practitioners long observed that triangular systems of eq

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The Challenge Posed by Long Transactions this result in full...  ..., .≥., ., . min.∥.−.∥ ............. ..  □.Replacing the Frobenius norm by the spectral norm, it follows from this backward stability result that the relative error for the computed solution . satisfies . and the loss of precision is bounded by . where .(.,.) is the normwi

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The Transcoop Specification Environment,s that we can find . as the solution of the system .=. with .:=..., ., and .:=.....A key remark at this stage is that by construction, . is symmetric and positive definite. One may therefore consider algorithms exploiting symmetry and positive definiteness. We do so in this chapter..The algorithms w

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Multi-Version Concurrency Revisited,also be done in terms of ., but in exchange for a loss of simplicity, we obtain bounds linear in . (instead of the quadratic dependence in . of the perceptron algorithm)..We also introduce in this chapter, in its last section, a new theme: the use of condition numbers in the analysis of algorithms t

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Transactions on Heterogeneous Hardware, more general context of linear programming. Succinctly described, the latter is a family of problems that consist in optimizing (i.e., maximizing or minimizing) a linear function over a set defined by linear . (equalities and/or inequalities)..A first step towards the solution of such a problem req

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Transaction-Level Power Modelingn 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

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