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A new class of parallel algorithms is introduced that can achieve a complexity of O(n^3/2) with respect to the interprocessor communication, in the exact computation of systems with pairwise mutual interactions of all elements. Hitherto,…
We solve principal component regression (PCR), up to a multiplicative accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$ black-box calls of ridge regression. Therefore, our algorithm does not require any explicit…
We consider a parallel computational model that consists of $P$ processors, each with a fast local ephemeral memory of limited size, and sharing a large persistent memory. The model allows for each processor to fault with bounded…
The envelope theory is a method to compute approximate eigensolutions of quantum $N$-body Hamiltonians with a quite general structure in $D$ dimensions. The advantages of the method are that it is easy to implement and that $N$ is treated…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
We consider the massively parallel computation (MPC) model, which is a theoretical abstraction of large-scale parallel processing models such as MapReduce. In this model, assuming the widely believed 1-vs-2-cycles conjecture, solving many…
This article presents the parallel implementation of the coupled harmonic oscillator. From the analytical solution of the coupled harmonic oscillator, the design parameters are obtained. After that, a numerical integration of the system…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
OpenMP is a cross-platform API that extends C, C++ and Fortran and provides shared-memory parallelism platform for those languages. The use of many cores and HPC technologies for scientific computing has been spread since the 1990s, and now…
Nested parallelism exists in scientific codes that are searching multi-dimensional spaces. However, implementations of nested parallelism often have overhead and load balance issues. The Orbital Analysis code we present exhibits a sparse…
We introduce a parallelizable simplification of Neural Turing Machine (NTM), referred to as P-NTM, which redesigns the core operations of the original architecture to enable efficient scan-based parallel execution. We evaluate the proposed…
We propose NEP_MiniMax, a novel computational method for solving nonlinear eigenvalue problems (NEPs) $T(\lambda)\mathbf{u}= 0$ on compact continua $\Omega \subset \mathbb{C}$. The method combines two key components: (1) a rational minimax…
The advent of efficient interior point optimization methods has enabled the tractable solution of large-scale linear and nonlinear programming (NLP) problems. A prominent example of such a method is seen in Ipopt, a widely-used, open-source…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Parallel processing is considered as todays and future trend for improving performance of computers. Computing devices ranging from small embedded systems to big clusters of computers rely on parallelizing applications to reduce execution…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
Mapping parallel threads onto non-box-shaped domains is a known challenge in GPU computing; efficient mapping prevents performance penalties from unnecessary resource allocation. Currently, achieving this requires significant analytical…
Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes $O(\sqrt{(\log n)/\varepsilon})$-approximation using…
In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…