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

Innovative

Interacting with the Execution Agent,ater 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

Constitution

Overview of Transaction Processing,this problem that can be efficiently tackled is that of linear systems of equations. What could be considered the level of difficulty immediately above that for linear systems, the case of quadratic, or more generally, polynomial equations, is substantially more complicated. Even for polynomials in

Feature

Normwise Condition of Linear Equation Solvinghis is called the . of ., and in numerical linear algebra, different ways for computing it are studied. From the QR factorization one obtains the solution of the system .=. by .=... and .=..., where the latter is easily computed by back substitution..The . is an algorithm for computing the QR-decomp

MAOIS

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Probabilistic Analysis of Rectangular Matrices 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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Linear Programs and Their Solution Sets 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