Related papers: Generalizing Frobenius Inversion to Quaternion Mat…

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…

In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…

Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…

Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…

Multiplicative inverse is a crucial operation in public key cryptography, and been widely used in cryptography. Public key cryptography has given rise to such a need, in which we need to generate a related public and private pair of…

We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…

We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…

Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…

In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…

Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present an algorithm to efficiently decide whether two polyadic…

In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…

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…

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…

We describe an explicit algorithm to factorize an even antisymmetric N^2 matrix into triangular and trivial factors. This allows for a straight forward computation of Pfaffians (including their signs) at the cost of N^3/3 flops.

In this paper, we address a new problem of reversing the effect of an image filter, which can be linear or nonlinear. The assumption is that the algorithm of the filter is unknown and the filter is available as a black box. We formulate…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…