The trace minimization method for the symmetric generalized eigenvalue problem

By A. Sameh, Zhanye Tong. 2000

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A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations (2007, unknown): “For example, denoting by M a symmetric deﬁnite positive matrix, the optimization problem on R could be deﬁned on the space of M -orthogonal matrices G is called a Stiefel manifold (cf. [26]).”
Atomistic Simulation of Realistically Sized Nanodevices Using NEMO 3-D—Part I: Models and Benchmarks (2007, methodology): “of the Lanczos method [39], the spectrum folding method [40], and the Tracemin [41].”
Generalized spectral decomposition method for solving stochastic finite element equations : Invariant subspace problem and dedicated algorithms (2008, methodology): “Remark 10 Due to homogeneity property of the generalized Rayleigh quotient, the optimization problem (34) can be interpreted as an optimization problem on Grasmann Manifold Grn,M [33].”
Trust-Region Methods on Riemannian Manifolds (2007, methodology): “The trace minimization method proposed by Sameh and Wisniewski [SW82, ST00 ] is constructed as follows.”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, background): “13 One can also introduce an associated generalized matrix Rayleigh quotient Σ(W ) [114], de ned by (Σ(W ))ij = A(W · f(W ), wifj(W )), and such σ(W ) = Trace(Σ(W )) (see [89,91]).”