Related papers: Computational Improvements to Matrix Operations
A factorization of the inverse of a Hermetian positive definite matrix based on a diagonal by diagonal recurrence formulae permits the inversion of Block Toeplitz matrices, using only matrix-vector products, and with a complexity of…
Matrix multiplications between asymmetric bit-width operands, especially between 8- and 4-bit operands are likely to become a fundamental kernel of many important workloads including neural networks and machine learning. While existing SIMD…
An optical neural network is proposed and demonstrated with programmable matrix transformation and nonlinear activation function of photodetection (square-law detection). Based on discrete phase-coherent spatial modes, the dimensionality of…
This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank property. This factorization approximates such a kernel matrix of…
Matrix-matrix multiplication is a key computational kernel for numerous applications in science and engineering, with ample parallelism and data locality that lends itself well to high-performance implementations. Many matrix…
On-chip optical neural networks (ONNs) have recently emerged as an attractive hardware accelerator for deep learning applications, characterized by high computing density, low latency, and compact size. As these networks rely heavily on…
This paper proposes an optimized mapping of the FIR filter algorithm that enhances the rate of a reconfigurable computer over a basic mapping previously proposed [1]. It also presents a new interconnection scheme in the reconfigurable part…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
Matrix-matrix multiplication is a key computational kernel for numerous applications in science and engineering, with ample parallelism and data locality that lends itself well to high-performance implementations. Many matrix…
Working in the multitape Turing model, we show how to reduce the problem of matrix transposition to the problem of integer multiplication. If transposing an $n \times n$ binary matrix requires $\Omega(n^2 \log n)$ steps on a Turing machine,…
Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated by matrices of low rank. A relatively general class of…
We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices and the recently proposed QTT format. The inverses of such matrices can be computed…
This paper shows that, for matrix multiplications and convolutions, it is possible to asymptotically replace each real multiplication with a single squaring operation. Similarly, a single complex multiplication can be replaced with 3…
In this paper, we present algorithms to solve matrix multiplication problems in the MPC model. In particular, we consider the problem under various processor/memory constraints in the MPC model and prove the following results. 1.…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
We show how to support efficient back traversal in a unidirectional list, using small memory and with essentially no slowdown in forward steps. Using $O(\log n)$ memory for a list of size $n$, the $i$'th back-step from the farthest point…
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
We present two fast algorithms for matrix-vector multiplication $y=Ax$, where $A$ is a Hankel matrix. The current asymptotically fastest method is based on the Fast Fourier Transform (FFT), however in multiprecision arithmetics with very…