Related papers: A hybrid Hermitian general eigenvalue solver
Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties which are pertinent to the entire sequence, and not just to the single problem. When such features take…
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…
A wide variety of outstanding problems in astrophysics involve the motion of a large number of particles ($N\gtrsim 10^{6}$) under the force of gravity. These include the global evolution of globular clusters, tidal disruptions of stars by…
Parallel computing is a standard approach to achieving high-performance computing (HPC). Three commonly used methods to implement parallel computing include: 1) applying multithreading technology on single-core or multi-core CPUs; 2)…
This work presents a GPU-accelerated solver for the unit commitment (UC) problem in large-scale power grids. The solver uses the Primal-Dual Hybrid Gradient (PDHG) algorithm to efficiently solve the relaxed linear subproblem, achieving…
Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…
Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this…
The High Performance Computing (HPC) field is witnessing a widespread adoption of Graphics Processing Units (GPUs) as co-processors for conventional homogeneous clusters. The adoption of prevalent Single- Program Multiple-Data (SPMD)…
Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate…
The linear response eigenvalue problem, which arises from many scientific and engineering fields, is quite challenging numerically for large-scale sparse/dense system, especially when it has zero eigenvalues. Based on a direct sum…
The Bethe-Salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized Bethe-Salpeter equation in the context of computing exciton energies and states. A computational challenge is that at least half of the…
The availability of low cost sensors has led to an unprecedented growth in the volume of spatial data. However, the time required to evaluate even simple spatial queries over large data sets greatly hampers our ability to interactively…
In the next decade, the demands for computing in large scientific experiments are expected to grow tremendously. During the same time period, CPU performance increases will be limited. At the CERN Large Hadron Collider (LHC), these two…
Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…
In this dissertation, we propose a memory and computing coordinated methodology to thoroughly exploit the characteristics and capabilities of the GPU-based heterogeneous system to effectively optimize applications' performance and privacy.…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
We describe randomized algorithms for computing the dominant eigenmodes of the Generalized Hermitian Eigenvalue Problem (GHEP) $Ax=\lambda Bx$, with $A$ Hermitian and $B$ Hermitian and positive definite. The algorithms we describe only…