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ORTHOGONAL POLYNOMIAL EXPANSIONS FOR SOLVING RANDOM EIGENVALUE PROBLEMS
9 references·16 citing·35 second hop
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this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2007Global sensitivity analysis using polynomial chaos expansions2,547 cited
  • 2004A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics441 cited
  • 2002An importance quantification technique in uncertainty analysis for computer models251 cited
  • 2008A polynomial dimensional decomposition for stochastic computing140 cited
  • 2006Random matrix eigenvalue problems in structural dynamics98 cited
  • 2005Analysis of Eigenvalues and Modal Interaction of Stochastic Systems80 cited
  • 2009Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions72 cited

Cited by

  • 2014Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing45 cited
  • 2016Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation44 cited
  • 2015Reliability-based design optimization by adaptive-sparse polynomial dimensional decomposition33 cited
  • 2012An invariant subspace‐based approach to the random eigenvalue problem of systems with clustered spectrum28 cited
  • 2013

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Karhunen–Loève decomposition of random fields based on a hierarchical matrix approach
27 cited
  • 2018Statistical moment analysis of nonlinear rotor system with multi uncertain variables27 cited
  • 2018Mathematical Properties of Polynomial Dimensional Decomposition26 cited
  • 2019Spectral stochastic isogeometric analysis of free vibration26 cited
  • 2018Uncertainty quantification under dependent random variables by a generalized polynomial dimensional decomposition25 cited
  • 2018A new point estimation method for statistical moments based on dimension-reduction method and direct numerical integration21 cited
  • 2014Stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty20 cited
  • 2018Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method19 cited
  • 2013Uncertainty quantification of high‐dimensional complex systems by multiplicative polynomial dimensional decompositions15 cited
  • 2018Functional ANOVA with Multiple Distributions: Implications for the Sensitivity Analysis of Computer Experiments14 cited
  • 2022An efficient reduced‐order method for stochastic eigenvalue analysis11 cited
  • 2016A surrogate method for density-based global sensitivity analysis11 cited