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The gap between the cost of moving data and the cost of computing continues to grow, making it ever harder to design iterative solvers on extreme-scale architectures. This problem can be alleviated by alternative algorithms that reduce the…
The problem of optimal precision switching for the conjugate gradient (CG) method applied to sparse linear systems is considered. A sparse matrix is defined as an $n\!\times\!n$ matrix with $m\!=\!O(n)$ nonzero entries. The algorithm first…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
With recent developments in parallel supercomputing architecture, many core, multi-core, and GPU processors are now commonplace, resulting in more levels of parallelism, memory hierarchy, and programming complexity. It has been necessary to…
A modern graphics processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two dimensional Ising model [T. Preis et al., J. Comp.…
Nowadays, subsequence similarity search is required in a wide range of time series mining applications: climate modeling, financial forecasts, medical research, etc. In most of these applications, the Dynamic TimeWarping (DTW) similarity…
We present new algorithms for the parallelization of Eulerian-Lagrangian interaction operations in the immersed boundary method. Our algorithms rely on two well-studied parallel primitives: key-value sort and segmented reduce. The use of…
Many computer systems for calculating the proper organization of memory are among the most critical issues. Using a tier cache memory (along with branching prediction) is an effective means of increasing modern multi-core processors'…
Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…
Parallel processing of information plays a critical role in accelerating computation. This includes quantum computers, where parallel processing of quantum information will play a critical role in practical quantum advantage. Here, we…
The introduction of Intel(R) Xeon Phi(TM) coprocessors opened up new possibilities in development of highly parallel applications. The familiarity and flexibility of the architecture together with compiler support integrated into the Intel…
Large Language Models (LLMs) demand substantial computational resources, resulting in high energy consumption on GPUs. To address this challenge, we focus on Coarse-Grained Reconfigurable Arrays (CGRAs) as an effective alternative that…
Nowadays, several industrial applications are being ported to parallel architectures. These applications take advantage of the potential parallelism provided by multiple core processors. Many-core processors, especially the GPUs(Graphics…
In this work, we consider the reformulation of hierarchical ($\mathcal{H}$) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal{H}$ matrices approximate specific dense…
The performance gains obtained by large language models (LLMs) are closely linked to their substantial computational and memory requirements. Quantized LLMs offer significant advantages with extremely quantized models, motivating the…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
Lattice QCD calculations were one of the first applications to show the potential of GPUs in the area of high performance computing. Our interest is to find ways to effectively use GPUs for lattice calculations using the overlap operator.…
Graph-based ANNS algorithms have gained increasing research interest and market adoption due to their efficiency and accuracy in retrieval. Existing approaches primarily rely on CPUs for graph index construction and retrieval, but this…
In this paper, we propose a 'full-stack' solution to designing high capacity and low latency on-chip cache hierarchies by starting at the circuit level of the hardware design stack. First, we propose a novel Gain Cell (GC) design using…
The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…