Multiplication of matrices

Fast multiplication of integer matrices Withdrawn paper

Erratum. Eric Schost discovered a bug in this paper: by construction, formula (7) does not hold, since the matrix Va,n is not invertible whenever l> 2. Unfortunately, we do not see how to repair this bug: not only Va,n is not invertible, but the rank of Va,n is actually very small (and equal to max {q1, , ql}). This makes the proof collapse. We have also tried a few other things, such as fixing...

Fast Multiplication of Matrices with Decay

A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize within the matrix space through truncation or rank reduction. Matrix truncation (element dropping) is compared to SpAMM for quantum chemical matrices with approxi...

Fast Multiplication of Interval Matrices (Interval Version of Strassen's Algorithm)

Multiplication of Matrices of ArbitraryShape on a Data

Some level{2 and level{3 Distributed Basic Linear Algebra Subroutines (DBLAS) that have been implemented on the Connection Machine system CM{200 are described. No assumption is made on the shape or size of the operands. For matrix{matrix multiplication , both the nonsystolic and the systolic algorithms are outlined. A systolic algorithm that computes the product matrix in{place is described in ...

Index of Hadamard Multiplication by Positive Matrices Ii

Given a definite nonnegative matrix A ∈ Mn(C), we study the minimal index of A : I(A) = max{λ ≥ 0 : A ◦ B ≥ λB for all 0 ≤ B}, where A ◦ B denotes the Hadamard product (A ◦ B)ij = AijBij . For any unitary invariant norm N in Mn(C), we consider the Nindex of A: I(N,A) = min{N(A ◦ B) : B ≥ 0 and N(B) = 1} If A has nonnegative entries, then I(A) = I(‖ · ‖sp, A) if and only if there exists a vector...