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Programmable unitary photonic devices are emerging as promising tools to implement unitary transformation for quantum information processing, machine learning, and optical communication. These devices typically use a rectangular mesh of…
With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are…
The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…
In many practical problems it is not necessary to compute the DFT in a perfect manner including some radar problems. In this article a new multiplication free algorithm for approximate computation of the DFT is introduced. All…
In the field of High Performance Computing, communications among processes represent a typical bottleneck for massively parallel scientific applications. Object of this research is the development of a network interface card with specific…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
Industry-grade database systems are expected to produce the same result if the same query is repeatedly run on the same input. However, the numerous sources of non-determinism in modern systems make reproducible results difficult to…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
Matrix multiplication is a fundamental kernel in large-scale artificial intelligence and scientific computing, but its performance on conventional electronic accelerators is increasingly constrained by memory bandwidth and energy…
Digital linear filters are used in a variety of applications (sound treatment, control/command, etc.), implemented in software, in hardware, or a combination thereof. For safety-critical applications, it is necessary to bound all variables…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular,…
Various approaches to the numerical representation of the Incomplete Gamma Function F_m(z) for complex arguments z and small integer indexes m are compared with respect to numerical fitness (accuracy and speed). We consider power series,…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
The rapid adoption of low-precision arithmetic in artificial intelligence and edge computing has created a strong demand for energy-efficient and flexible floating-point multiply-accumulate (MAC) units. This paper presents a dual-precision…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
The state-of-the-art (SOTA) for mixed precision training is dominated by variants of low precision floating point operations, and in particular, FP16 accumulating into FP32 Micikevicius et al. (2017). On the other hand, while a lot of…
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…
In the field of digital signal processing, the fast Fourier transform (FFT) is a fundamental algorithm, with its processors being implemented using either the pipelined architecture, well-known for high-throughput applications but weak in…