Related papers: Algorithm 1019: A Task-based Multi-shift QR/QZ Alg…
Embedded computer vision applications increasingly require the speed and power benefits of single-precision (32 bit) floating point. However, applications which make use of Levenberg-like optimization can lose significant accuracy when…
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
Quantum data encoding (QDE) enables faster com-putations than classical algorithms through superposition and en-tanglement. Circuit cutting and knitting are effective techniques for ameliorating current noisy quantum processing unit (QPUs)…
In this paper we present an improved dqds algorithm for computing all the singular values of a bidiagonal matrix to high relative accuracy. There are two key contributions: a novel deflation strategy that improves the convergence for badly…
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the…
Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here,…
Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes…
We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
High-dimensional numerical optimization presents a persistent challenge in computational science. This paper introduces Quasi-Adaptive Search with Asymptotic Reinitialization (QUASAR), an evolutionary algorithm to accelerate convergence in…
A q-Levenberg-Marquardt method is an iterative procedure that blends a q-steepest descent and q-Gauss-Newton methods. When the current solution is far from the correct one the algorithm acts as the q-steepest descent method. Otherwise the…
In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…
Reinforcement learning (RL) for complex tasks remains a challenge, primarily due to the difficulties of engineering scalar reward functions and the inherent inefficiency of training models from scratch. Instead, it would be better to…
This paper considers clustered multi-task compressive sensing, a hierarchical model that solves multiple compressive sensing tasks by finding clusters of tasks that leverage shared information to mutually improve signal reconstruction. The…
Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Quantization is a widely used technique to compress and accelerate deep neural networks. However, conventional quantization methods use the same bit-width for all (or most of) the layers, which often suffer significant accuracy degradation…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
We consider the Linear-Quadratic-Regulator (LQR) problem in terms of optimizing a real-valued matrix function over the set of feedback gains. Such a setup facilitates examining the implications of a natural initial-state independent…