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This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for…
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice…
Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by…
We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic…
Continuing earlier work of the first author with U. Berger, K. Miyamoto and H. Tsuiki, it is shown how a division algorithm for real numbers given as a stream of signed digits can be extracted from an appropriate formal proof. The property…
In this paper, we present multi-threaded algorithms for graph coloring suitable to the shared memory programming model. We modify an existing algorithm widely used in the literature and prove the correctness of the modified algorithm. We…
Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput…
Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formulations, relaxation and coarse-graining are analyzed and…
We develop a full-fledged analysis of an algorithmic decision process that, in a multialternative choice problem, produces computable choice probabilities and expected decision times.
Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations,…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction $\Pi$ will…
We present the new multi-threaded version of the state-of-the-art answer set solver clasp. We detail its component and communication architecture and illustrate how they support the principal functionalities of clasp. Also, we provide some…
In this paper we consider the matrix structure of arithmetic processors based on distributed arithmetic in multi-row codes. Scope - development of supercomputers.
In this study, we propose a novel computing paradigm "Bit Stream Computing" that is constructed on the logic used in stochastic computing, but does not necessarily employ randomly or Binomially distributed bit streams as stochastic…
Modern graphics computing units (GPUs) are designed and optimized to perform highly parallel numerical calculations. This parallelism has enabled (and promises) significant advantages, both in terms of energy performance and calculation. In…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
We extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated at three loops in gauge theories with any number…
Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or…
Counterfactual explanations is one of the post-hoc methods used to provide explainability to machine learning models that have been attracting attention in recent years. Most examples in the literature, address the problem of generating…