Related papers: ChASE: Chebyshev Accelerated Subspace iteration Ei…

We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral…

The FEAST algorithm is a subspace iteration method that uses a spectral projector as a rational filter in order to efficiently solve interior eigenvalue problems in parallel. Although the solutions from the FEAST algorithm converge rapidly…

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…

In Density Functional Theory simulations based on the LAPW method, each self-consistent field cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space methods, eigenpairs solving for problems at distinct…

We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior…

We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…

It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, etc. The subspace iteration is a kind of widely used…

The FEAST library package represents an unified framework for solving various family of eigenvalue problems and achieving accuracy, robustness, high-performance and scalability on parallel architectures. Its originality lies with a new…

We consider the problem of parallelizing electronic structure computations in plane-wave Density Functional Theory. Because of the limited scalability of Fourier transforms, parallelism has to be found at the eigensolver level. We show how…

We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…

Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The…

Homomorphic Encryption (HE) is one of the most promising security solutions to emerging Machine Learning as a Service (MLaaS). Leveled-HE (LHE)-enabled Convolutional Neural Networks (LHECNNs) are proposed to implement MLaaS to avoid large…

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…

Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be…

New computing paradigms are required to solve the most challenging computational problems where no exact polynomial time solution exists.Probabilistic Ising Accelerators has gained promise on these problems with the ability to model complex…

As the application of deep learning continues to grow, so does the amount of data used to make predictions. While traditionally, big-data deep learning was constrained by computing performance and off-chip memory bandwidth, a new constraint…

We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…

The FEAST eigensolver is extended to the computation of the singular triplets of a large matrix $A$ with the singular values in a given interval. The resulting FEAST SVDsolver is subspace iteration applied to an approximate spectral…

The solution of (generalized) eigenvalue problems for symmetric or Hermitian matrices is a common subtask of many numerical calculations in electronic structure theory or materials science. Solving the eigenvalue problem can easily amount…