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Compared with several state-of-the-art methods, preliminary numerical experiments on solving the Q-weighted low-rank correlation matrix problem from finance validate the efficiency of the proposed method.
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Second, the plethora of genetic markers obtained from different genotyping platforms has resurrected the "empty matrix" problem, whereby populations from different studies can barely be compared due to the low overlap of these platforms.
At the same time, however, when used for samples having a complex matrix, problems resulting from low recovery of analytes and low reproducibility of results due to nonselective and incomplete desorption can arise.
The method is illustrated for a small size matrix from an affine matrix problem and is then applied to large matrices actually arising from more sophisticated control problems used in the design of the Boeing 767 jet and a nuclear powered turbo-generator.
However, conventional method suffers from high complexity and singular matrix problem.
In this paper, we propose a novel recursive contour integral method for matrix eigenvalue problems from finite element discretizations of transmission eigenvalue problems.
The use of Householder transformation can not only preserve orthogonality, but also turn the problem from a matrix optimization into a vector optimization problem.
In the first step a quadratic matrix eigenvalue problem resulting from the minimization of a discrete residual error function is solved.
Step 1: It is dedicated to the deduction of POI matrix from the problem data.
By using Eq. (7), optimization-based algorithm is able to recover the row-sparse matrix from the problem defined by: widehat{X}=underset{Xin {mathrm{mathbb{R}}}^{Ntimes L}}{ min }{leftVert XrightVert}_{2,1} s. t.kern0.5em {leftVert Y-Phi XrightVert}_2^2
The method is especially applicable to matrix eigenvalue problems that arise from the discretization of self-adjoint partial differential equations.
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