Related papers: Acceleration of complex matrix multiplication usin…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
Linear algebra routines are basic building blocks for the statistical software. In this paper we analyzed how can we can improve R performance for matrix computations. We benchmarked few matrix operations using the standard linear algebra…
The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…
This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication algorithms with ternary coefficients $\{-1,0,1\}$. The approach replaces expensive exact evaluation with fast heuristic…
Sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it…
We study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of $P$ computation nodes where each node stores $1/m$ of each multiplicand via linear encoding. Our main result shows that the…
This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…
Current Python programming environment does not have any reliable and efficient multiple precision floating-point (MPF) arithmetic except ``mpmath" and ``gmpy2" packages based on GNU MP(GMP) and MPFR libraries. Although it is well known…
The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based…
We propose a more accurate variant of an algorithm for multiplying 4x4 matrices using 48 multiplications over any ring containing an inverse of 2. This algorithm has an error bound exponent of only log 4 $\gamma$$\infty$,2 $\approx$ 2.386.…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (GF(2)). In particular we present our implementation -- in the M4RI library -- of Strassen-Winograd…
In 1969, V. Strassen improves the classical~2x2 matrix multiplication algorithm. The current upper bound for 3x3 matrix multiplication was reached by J.B. Laderman in 1976. This note presents a geometric relationship between Strassen and…
Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by…
Sparse matrices have recently played a significant and impactful role in scientific computing, including artificial intelligence-related fields. According to historical studies on sparse matrix--vector multiplication (SpMV), Krylov subspace…
Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm…
The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, the cost of matrix multiplication associated with this…
Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…