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Solving sparse linear systems lies at the core of numerous computational applications. Consequently, understanding the performance of recently proposed alternatives to the established IEEE 754 floating-point numbers, such as bfloat16 and…

The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…

Recent evaluations have highlighted the tapered posit number format as a promising alternative to the uniform precision IEEE 754 floating-point numbers, which suffer from various deficiencies. Although the posit encoding scheme offers…

Although not primarily designed for this purpose, floating-point numbers are often used to represent integral values, with some applications explicitly relying on this capability. However, the integral representation properties of IEEE 754…

In light of recent hardware advances, it is striking that real arithmetic in balanced ternary logic has received almost no attention in the literature. This is particularly surprising given ternary logic's promising properties, which could…

This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation $Ax =…

In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with sufficiently small backward errors, the magnitude of the resulting…

Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…

This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…

In modern low-power embedded platforms, floating-point (FP) operations emerge as a major contributor to the energy consumption of compute-intensive applications with large dynamic range. Experimental evidence shows that 50% of the energy…

Statistical computations are becoming increasingly important. These computations often need to be performed in log-space because probabilities become extremely small due to repeated multiplications. While using logarithms effectively…

Motivated by the increasing interest in the posit numeric format, in this paper we evaluate the accuracy and efficiency of posit arithmetic in contrast to the traditional IEEE 754 32-bit floating-point (FP32) arithmetic. We first design and…

In recent years, a great deal of attention has been focused on numerically solving exponential integrators. The important ingredient to the implementation of exponential integrators is the efficient and accurate evaluation of the so called…

In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…

The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a…

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…

The Arnoldi process provides an efficient framework for approximating functions of a matrix applied to a vector, i.e., of the form $f(M)\bm{b}$, by repeated matrix-vector multiplications. In this paper, we derive error estimates for…

Mixing precisions for performance has been an ongoing trend as the modern hardware accelerators started including new, and mostly lower-precision, data formats. The advantage of using them is a great potential of performance gain and energy…

The growing demand for edge-AI systems requires arithmetic units that balance numerical precision, energy efficiency, and compact hardware while supporting diverse formats. Posit arithmetic offers advantages over floating- and fixed-point…

We present an exact sampling algorithm for Pfaffian point processes based on a skew-symmetric analogue of the Cholesky factorization. This algorithm enables efficient sampling of a wide range of statistics arising in random matrix theory…