Related papers: An Error-Resilient Redundant Subspace Correction M…

Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…

We present CLEAR (Cross-Layer Exploration for Architecting Resilience), a first of its kind framework which overcomes a major challenge in the design of digital systems that are resilient to reliability failures: achieve desired resilience…

Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…

Serial-parallel redundancy is a reliable way to ensure service and systems will be available in cloud computing. That method involves making copies of the same system or program, with only one remaining active. When an error occurs, the…

An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…

Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…

The ever growing demands of embedded systems to satisfy high computing performance and cost efficiency lead to the trend of using commercial off-the-shelf hardware. However, due to their highly integrated design they are becoming…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

With the rapid advancements of deep learning in the past decade, it can be foreseen that deep learning will be continuously deployed in more and more safety-critical applications such as autonomous driving and robotics. In this context,…

Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…

Modeling the dynamic behavior of deformable objects is crucial for creating realistic digital worlds. While conventional simulations produce high-quality motions, their computational costs are often prohibitive. Subspace simulation…

This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…

Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…

As supercomputers grow in hardware complexity, their susceptibility to faults increases and measures need to be taken to ensure the correctness of results. Some numerical algorithms have certain characteristics that allow them to recover…

Modern computationally-intensive applications often operate under time constraints, necessitating acceleration methods and distribution of computational workloads across multiple entities. However, the outcome is either achieved within the…

Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…

A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

Computational efficiency has remained a critical consideration in scaling high-capacity language models, with inference latency and resource consumption presenting significant constraints on real-time applications. The study has introduced…