Furthermore, a new algorithm for matrix partitioning that significantly reduces the number of blocks generated is presented.doi:10.1007/s00607-002-1469-6M. BebendorfS. RjasanowSpringer-VerlagComputingBebendorf, M. , and S.Rjasanow ( 2003 ), Adaptive low-rank approximation of ...
摘要: BIT Numerical Mathematics - Dynamical low-rank integrators for matrix differential equations recently attracted a lot of attention and have proven to be very efficient in various applications. In...关键词: Dynamical low-rank approximation Matrix differential equations Rank-adaptivity 65L04 65L05 ...
We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and ...
It is important to notice that this low rank approximation is not related to the rank reduction step performed by the adaptive algorithms. Finally, we separate the noise and signal subspace using the dewhitening step, which means multiplying it by the estimated correlation factor matrix Lˆ. ...
Structure-guided shape-preserving mesh texture smoothing via joint low-rank matrix recovery. Comput. Aided Des. 2019, 115, 122–134. [Google Scholar] [CrossRef] Lu, X.; Schaefer, S.; Luo, J.; Ma, L.; He, Y. Low rank matrix approximation for 3D geometry filtering. IEEE Trans. Vis....
The approach involves dividing the image into blocks using a sliding window, followed by vectorizing the block matrices and rearranging them into a data matrix. Robust principal component analysis (RPCA) is employed to decompose the data matrix into a low-rank matrix and a sparse matrix. Finally...
The corresponding low-rank adaptive filter requires only O(Nr) operations per time step, where r⩽N denotes the rank of the data covariance matrix. Thus, low-rank adaptive filters can be computationally less (or even much less) demanding, depending on the order/rank ratio N/r or the ...
In this section, a robust subspace clustering model (LAKRSC) is proposed, which joint non-convex low-rank approximation and adaptive kernel. Firstly, we formulate the objective function of LAKRSC. Second, an effective optimization algorithm (HQ&ADMM) is proposed. ...
The weights in the optimum STAP technique can be naturally expressible as the weight matrix. An efficient dimension-reduced space-time adaptive clutter suppression (STACS) algorithm based on lower-rank approximation to weight matrix is established, which finds a set of space-time separable filters ...
(rn 2 ),whereristherankoftherepresentationmatrix.Numericalexperiments verifythatforLRRourLADMAPmethodismuchfasterthanstate-of-the-artal- gorithms.AlthoughweonlypresenttheresultsonLRR,LADMAPactuallycan beappliedtosolvingmoregeneralconvexprograms. 1Introduction Recently,compressivesensing[5]andsparserepresentation[...