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Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…

Numerical Analysis · Mathematics 2019-10-09 Jehanzeb Chaudhry , Don Estep , Simon Tavener

Supercomputing systems today often come in the form of large numbers of commodity systems linked together into a computing cluster. These systems, like any distributed system, can have large numbers of independent hardware components…

Distributed, Parallel, and Cluster Computing · Computer Science 2007-05-23 Michael Treaster

Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to…

Signal Processing · Electrical Eng. & Systems 2025-02-06 Shuche Wang , Vincent Y. F. Tan

Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g. superconducting circuits or quantum dots, is studied in this paper. Errors caused by topologically…

Quantum Physics · Physics 2016-09-21 Ying Li

Sparse linear systems are typically solved using preconditioned iterative methods, but applying preconditioners via sparse triangular solves introduces bottlenecks due to irregular memory accesses and data dependencies. This work leverages…

Performance · Computer Science 2025-08-08 Atharva Gondhalekar , Kjetil Haugen , Thomas Gibson , Wu-chun Feng

We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…

Numerical Analysis · Mathematics 2026-03-11 Stephan Köhler , Oliver Rheinbach , Yue Xiang Tee , Sebastian Zug

In this paper we do a detailed numerical investigation of the fault-tolerant threshold for optical cluster-state quantum computation. Our noise model allows both photon loss and depolarizing noise, as a general proxy for all types of local…

Quantum Physics · Physics 2009-11-13 Christopher M. Dawson , Henry L. Haselgrove , Michael A. Nielsen

Machine learning systems in fraud detection, credit scoring, and clinical risk assessment operate under delayed ground truth: outcome labels arrive days to months after the decision they evaluate. During this blind period, governance…

Computers and Society · Computer Science 2026-04-20 Oleg Solozobov

We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing…

Quantum Physics · Physics 2018-01-08 Christopher Chamberland , Pavithran Iyer , David Poulin

The idle computers on a local area, campus area, or even wide area network represent a significant computational resource---one that is, however, also unreliable, heterogeneous, and opportunistic. This type of resource has been used…

Distributed, Parallel, and Cluster Computing · Computer Science 2007-05-23 Adriana Iamnitchi , Ian Foster

Krylov subspace methods are linear solvers based on matrix-vector multiplications and vector operations. While easily parallelizable, they are sensitive to rounding errors and may experience convergence issues. ILU(0), an incomplete LU…

Numerical Analysis · Mathematics 2025-07-10 Tomonori Kouya

In this paper, a novel approach, Inforence, is proposed to isolate the suspicious codes that likely contain faults. Inforence employs a feature selection method, based on mutual information, to identify those bug-related statements that may…

Software Engineering · Computer Science 2017-12-12 Farid Feyzi , Saeed Parsa

In today's era of big data, robust least-squares regression becomes a more challenging problem when considering the adversarial corruption along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer…

Data Structures and Algorithms · Computer Science 2017-10-04 Xuchao Zhang , Liang Zhao , Arnold P. Boedihardjo , Chang-Tien Lu

Solving optimization problems with transient PDE-constraints is computationally costly due to the number of nonlinear iterations and the cost of solving large-scale KKT matrices. These matrices scale with the size of the spatial…

Numerical Analysis · Mathematics 2023-05-09 Eric C. Cyr

Fully Homomorphic Encryption (FHE) is rapidly emerging as a promising foundation for privacy-preserving cloud services, enabling computation directly on encrypted data. As FHE implementations mature and begin moving toward practical…

Cryptography and Security · Computer Science 2026-03-25 Jianan Mu , Ge Yu , Zhaoxuan Kan , Song Bian , Liang Kong , Zizhen Liu , Cheng Liu , Jing Ye , Huawei Li

Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully…

Numerical Analysis · Mathematics 2020-11-12 Sven Baars , Mark van der Klok , Jonas Thies , Fred W. Wubs

We study the problem of fault isolation in linear systems with actuator and sensor faults within a data-driven framework. We propose a nullspace-based filter that uses solely fault-free input-output data collected under process and…

Systems and Control · Electrical Eng. & Systems 2026-05-25 Mohammad Amin Sheikhi , Gabriel de Albuquerque Gleizer , Peyman Mohajerin Esfahani , Tamás Keviczky

Obfuscation stands as a promising solution for safeguarding hardware intellectual property (IP) against a spectrum of threats including reverse engineering, IP piracy, and tampering. In this paper, we introduce Obfus-chat, a novel framework…

Future extreme-scale computer systems may expose silent data corruption (SDC) to applications, in order to save energy or increase performance. However, resilience research struggles to come up with useful abstract programming models for…

Mathematical Software · Computer Science 2014-01-15 James Elliott , Mark Hoemmen , Frank Mueller

As Large Language Models (LLMs) are increasingly deployed in mission-critical software systems, detecting hallucinations and ``faked truthfulness'' has become a paramount engineering challenge. Current reliability architectures rely heavily…

Software Engineering · Computer Science 2026-04-16 Jonathan Pan