Related papers: Faster Inversion and Other Black Box Matrix Comput…
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected $O\big(n^{2.2131}\big)$ time for the current values of fast rectangular matrix multiplication. We achieve the same…
We present algorithms to compute the Smith Normal Form of matrices over two families of local rings. The algorithms use the \emph{black-box} model which is suitable for sparse and structured matrices. The algorithms depend on a number of…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…
Large-scale machine learning (ML) models are increasingly being used in critical domains like education, lending, recruitment, healthcare, criminal justice, etc. However, the training, deployment, and utilization of these models demand…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
We introduce an algorithm for efficiently representing convolution with zero-padding and stride as a sparse transformation matrix, applied to a vectorized input through sparse matrix-vector multiplication (SpMV). We provide a theoretical…
The growth of big data in domains such as Earth Sciences, Social Networks, Physical Sciences, etc. has lead to an immense need for efficient and scalable linear algebra operations, e.g. Matrix inversion. Existing methods for efficient and…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…
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…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator \cite{liu2015fast} and derive its…
Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…
This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix $A^{n \times d}$ one by one in the…
For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…