Hierarchical Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations

Graph Problems and Vector-Matrix Multiplications in Haskell

It is a known fact that many graph problems can be restated in terms of an algebraic setting. One particular operation that arises in such a setting is the multiplication of a vector with a matrix. Depending on the underlying algebra the multiplication can carry different reachability semantics (e.g. no additional information, single path prolongation, all path prolongation). We propose an abst...

Fast construction of hierarchical matrix representation from matrix-vector multiplication

We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses OðlognÞ applications of the matrix on structured random test vectors and Oðn lognÞ extra computational cost, where n is the dimension of the unknown matrix. Numerical examples on constructing Green’s functions ...

Systolic arrays for matrix multiplications

Matrix-Matrix Multiplications and Fault Tolerance on Hypercube Multiprocessors

Several new algorithms for matrix-matrix multiplications on hypercube multiprocessors are presented and evaluated based on the number of multiplications, additions, and transfers. The matrices ~I be multiplied are uniformly distributed to all processors of a hypercube system. Each processor owns some submatrices which are derived by dividing the source matrices. Each submatrix multiplication ca...

"Wide or tall" and "sparse matrix dense matrix" multiplications

This note explores sparse matrix dense matrix (SMDM) multiplications, useful in block Krylov or block Lanczos methods. SMDM computations are AU , and V A, multiplication of a large sparse matrix m × n matrix A by a matrix V of k rows of length m or a matrix U of k columns of length k, k << m, k << n . In a block Lanczos or Krylov algorithm, matrix matrix multiplications with the ”tall” U and ”w...