Stochastic Algebraic Equations

Mircea Grigoriu ()
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Mircea Grigoriu: Cornell University

Chapter Chapter 8 in Stochastic Systems, 2012, pp 337-378 from Springer

Abstract: Abstract Methods are discussed for solving approximately linear algebraic equations with random parameters, referred to as stochastic algebraic equations (SAEs). Section 8.1 defines SAEs and outlines potential difficulties related to the solution of these equations. Section 8.2 presents solutions of SAEs with random entries of arbitrary uncertainty by Monte Carlo simulation, stochastic reduced order models, stochastic Galerkin, stochastic collocation, and reliability methods. SAEs with random entries of small uncertainty are solved in Section 8.3 by Taylor series, perturbation, Neumann series, and equivalent linearization methods.

Keywords: Weak Solution; Random Parameter; Collocation Point; Bernstein Polynomial; Monte Carlo Estimate (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4471-2327-9_8

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