Related papers: An Improvement in Quantum Fourier Transform

In this paper, an accurate direction-of-arrival (DOA) estimator is developed based on the real-valued singular value decomposition (SVD) of covariance matrix. Unitary transform on the complex-valued covariance matrix is first applied, and…

Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…

This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…

Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…

Quantum singular value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms. In this work, we leverage the QSVT framework in two directions. We first show that the QSVT framework can…

Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…

Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two…

The eigenvalue decomposition (EVD) of (a batch of) Hermitian matrices of order two has a role in many numerical algorithms, of which the one-sided Jacobi method for the singular value decomposition (SVD) is the prime example. In this paper…

Modeling quantum interference in the presence of dissipation is a critical aspect of quantum technologies. Including dissipation into the model of a linear device enables for assesing the detrimental impact of photon loss, as well as for…

Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on…

The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…

The Quantum Singular Value Transformation (QSVT) is a recent technique that gives a unified framework to describe most quantum algorithms discovered so far, and may lead to the development of novel quantum algorithms. In this paper we…

Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying…

In a Jacobi--Davidson (JD) type method for singular value decomposition (SVD) problems, called JDSVD, a large symmetric and generally indefinite correction equation is solved iteratively at each outer iteration, which constitutes the inner…

Intraoperative 2D quantitative angiography (QA) for intracranial aneurysms (IAs) has accuracy challenges due to the variability of hand injections. Despite the success of singular value decomposition (SVD) algorithms in reducing biases in…

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

Efficiently computing a subset of a correlation matrix consisting of values above a specified threshold is important to many practical applications. Real-world problems in genomics, machine learning, finance other applications can produce…

We present two generalisations of Singular Value Decomposition from real-numbered matrices to dual-numbered matrices. We prove that every dual-numbered matrix has both types of SVD. Both of our generalisations are motivated by applications,…

A promising area of applications for quantum computing is in linear algebra problems. In this work, we introduce two new quantum t-SVD (tensor-SVD) algorithms. The first algorithm is largely based on previous work that proposed a quantum…

Singular value decomposition (SVD) is widely used in wireless systems, including multiple-input multiple-output (MIMO) processing and dimension reduction in distributed MIMO (D-MIMO). However, the iterative nature of decomposition methods…