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Probabilistic analysis of condition numbers
Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011Condition numbers are well known in numerical linear algebra. It is less known that this concept also plays a crucial part in understanding the efficiency of algorithms in linear programming, convex optimization, and for solving systems of polynomial equations. Indeed, the running time of such algorithms may be often effectively bounded in terms of the
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Probabilistic analyses of condition numbers
Acta Numerica, 2016In recent decades, condition numbers have joined forces with probabilistic analysis to give rise to a form of condition-based analysis of algorithms. In this paper we survey how this analysis is done via a number of examples. We precede this catalogue of examples with short primers on both condition numbers and probabilistic analyses.
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On Condition Number Theorems in Mathematical Programming
Journal of Optimization Theory and Applications, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonnormality and Jordan Condition Numbers of Matrices
Journal of the ACM, 1969A lower bound for the departure from normality of an n X n matrix A is given. Furthermore, various inequalities are obtained for certain condition numbers associated with the reduction of A to its Jordan canonical form.
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On the conditional laws of large numbers. I.
Publicationes Mathematicae Debrecen, 2022openaire +1 more source