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Dijkstra observed that verifying correctness of a program is difficult and conjectured that derivation of a program hand-in-hand with its proof of correctness was the answer. We illustrate this goal-oriented approach by applying it to the…
Tropical algebra, including max-plus, min-plus, and related idempotent semirings, provides a unifying framework in which many optimization problems that are nonlinear in classical algebra become linear. This property makes tropical methods…
We approach the problem of implementing mixed-datatype support within the general matrix multiplication (GEMM) operation of the BLIS framework, whereby each matrix operand A, B, and C may be stored as single- or double-precision real or…
Linear algebra operations are widely used in scientific computing and machine learning applications. However, it is challenging for scientists and data analysts to run linear algebra at scales beyond a single machine. Traditional approaches…
Furthering our understanding of many of today's interesting problems in plasma physics---including plasma based acceleration and magnetic reconnection with pair production due to quantum electrodynamic effects---requires large-scale kinetic…
Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph…
Scientific applications are often complex, irregular, and computationally-intensive. To accommodate the ever-increasing computational demands of scientific applications, high-performance computing (HPC) systems have become larger and more…
Combinatorial algorithms such as those that arise in graph analysis, modeling of discrete systems, bioinformatics, and chemistry, are often hard to parallelize. The Combinatorial BLAS library implements key computational primitives for…
This dissertation introduces measurement-based performance modeling and prediction techniques for dense linear algebra algorithms. As a core principle, these techniques avoid executions of such algorithms entirely, and instead predict their…
Data centers handle vast volumes of data that require efficient lossless compression, yet emerging probabilistic models based methods are often computationally slow. To address this, we introduce RAS, the Range Asymmetric Numeral System…
A new generation of manycore processors is on the rise that offers dozens and more cores on a chip and, in a sense, fuses host processor and accelerator. In this paper we target the efficient training of generalized linear models on these…
The limited number of qubits per chip remains a critical bottleneck in quantum computing, motivating the use of distributed architectures that interconnect multiple quantum processing units (QPUs). However, executing quantum algorithms…
High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel…
Large language models (LLMs) exhibit memory-intensive behavior during decoding, making it a key bottleneck in LLM inference. To accelerate decoding execution, hybrid-bonding-based 3D-DRAM has been adopted in LLM accelerators. While this…
Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…
This paper presents the XAMG library for solving large sparse systems of linear algebraic equations with multiple right-hand side vectors. The library specializes but is not limited to the solution of linear systems obtained from the…
The current workloads and applications are highly diversified, facing critical challenges such as the Power Wall and the Memory Wall Problem. Different strategies over the multiple levels of Caches have evolved to mitigate these problems.…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…
The integration of large language models (LLMs) with external tools has significantly expanded the capabilities of AI agents. However, as the diversity of both LLMs and tools increases, selecting the optimal model-tool combination becomes a…
Energy-efficiency has become a major challenge in modern computer systems. To address this challenge, candidate systems increasingly integrate heterogeneous cores in order to satisfy diverse computation requirements by selecting cores with…