Related papers: CPQR-based randomized algorithms for generalized C…
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
Deterministic recursive algorithms for the computation of matrix triangular decompositions with permutations like LU and Bruhat decomposition are presented for the case of commutative domains. This decomposition can be considered as a…
The canonical polyadic (CP) decomposition is one of the most widely used tensor decomposition techniques. The conventional CP decomposition algorithm combines alternating least squares (ALS) with the normal equation. However, the normal…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix…
We propose a generalized CUR (GCUR) decomposition for matrix pairs $(A, B)$. Given matrices $A$ and $B$ with the same number of columns, such a decomposition provides low-rank approximations of both matrices simultaneously, in terms of some…
Given a matrix $A$ of size $m\times n$, the manuscript describes a algorithm for computing a QR factorization $AP=QR$ where $P$ is a permutation matrix, $Q$ is orthonormal, and $R$ is upper triangular. The algorithm is blocked, to allow it…
Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…
We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
This paper presents a fault-tolerant algorithm for the QR factorization of general matrices. It relies on the communication-avoiding algorithm, and uses the structure of the reduction of each part of the computation to introduce…
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample…
Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables. In…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
While the proper orthogonal decomposition (POD) is optimal under certain norms it's also expensive to compute. For large matrix sizes, it is well known that the QR decomposition provides a tractable alternative. Under the assumption that it…
A low-rank approximation of a parameter-dependent matrix $A(t)$ is an important task in the computational sciences appearing for example in dynamical systems and compression of a series of images. In this work, we introduce AdaCUR, an…