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- articleMarch 2012
Riemannian Optimization on Tensor Products of Grassmann Manifolds: Applications to Generalized Rayleigh-Quotients
SIAM Journal on Matrix Analysis and Applications (SIMAX), Volume 33, Issue 1Pages 210–234https://doi.org/10.1137/100792032We introduce a generalized Rayleigh-quotient $\rho_A$ on the direct product of Grassmannians $\mathrm{Gr}({\bf m},{\bf n})$ enabling a unified approach to well-known optimization tasks from different areas of numerical linear algebra, such as best low-...
- ArticleFebruary 2012
A Conjugated Gradient Method for Bound Constrained Optimization
IC3T '12: Proceedings of the 2012 International Conference on Convergence Computer TechnologyPages 124–127A algorithm for solving nonlinear optimization problems with simple bounds is described. The constraint is treated with the gradient projection method. The applied line search technology couples the monotone line search technology and nonmonotone line ...
- articleJuly 1995
Radiosity and hybrid methods
ACM Transactions on Graphics (TOG), Volume 14, Issue 3Pages 233–265https://doi.org/10.1145/212332.212347We examine various solutions to the global illumination problem, based on an exact mathematical analysis of the rendering equation. In addition to introducing efficient radiosity algorithms, we present a uniform approach to reformulate all of the basic ...