We consider the problem of solving linear systems of equations with limited-memory members of the restricted Broyden class and symmetric rank-one matrices. In this paper, we present various methods for solving these linear systems, and propose a new approach based on a practical implementation of the compact representation for the inverse of these limited-memory matrices. Using the proposed app...

The paper presents a new algorithm FPPR which updates PageRanks of directed network after topological changes in the graphs. is capable regenerating scores on node and link addition/deletion. expected value random surfers are used for updating newly added nodes as well impacted chain where nodes/links or removed. complexity k addition $$\mathcal {O}(k\times d^{(k)}_{avg})$$ $$d^{(k)}_{avg}$$ av...

In low-rank & sparse matrix decomposition, the entries of the sparse part are often assumed to be i.i.d. sampled from a random distribution. But the structure of sparse part, as the central interest of many problems, has been rarely studied. One motivating problem is tracking multiple sparse object flows (motions) in video. We introduce “shifted subspaces tracking (SST)” to segment the motions ...

We investigate the use of the SMPSs programming model to leverage task parallelism in the execution of a message-passing implementation of the symmetric rank-k update on clusters equipped with multicore processors. Our experience shows that the major difficulties to adapt the code to the MPI/SMPSs instance of this programming model are due to the usage of the conventional column-major layout of...

Given a sparse symmetric positive definite matrix AAT and an associated sparse Cholesky factorization LDLT or LLT, we develop sparse techniques for updating the factorization after either adding a collection of columns to A or deleting a collection of columns from A. Our techniques are based on an analysis and manipulation of the underlying graph structure, using the framework developed in an e...