Related papers: Efficient Non-sequential Division for FPGAs
Due to the emergence of embedded applications in image and video processing, communication and cryptography, improvement of pictorial information for better human perception like deblurring, denoising in several fields such as satellite…
This thesis develops signal-processing algorithms and implementation schemes under constraints of minimal parallelism and memory space, with the goal of improving energy efficiency of low-power computing hardware. We propose (i) a…
This work explores an unexpected application of Implicit Computational Complexity (ICC) to parallelize loops in imperative programs. Thanks to a lightweight dependency analysis, our algorithm allows splitting a loop into multiple loops that…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
A unified fast time-stepping method for both fractional integral and derivative operators is proposed. The fractional operator is decomposed into a local part with memory length $\Delta T$ and a history part, where the local part is…
Improving the computational efficiency of quantum many-body calculations from a hardware perspective remains a critical challenge. Although field-programmable gate arrays (FPGAs) have recently been exploited to improve the computational…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
To achieve systematic generalisation, it first makes sense to master simple tasks such as arithmetic. Of the four fundamental arithmetic operations (+,-,$\times$,$\div$), division is considered the most difficult for both humans and…
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
We propose and analyze a versatile and general algorithm called nonlinear forward-backward splitting (NOFOB). The algorithm consists of two steps; first an evaluation of a nonlinear forward-backward map followed by a relaxed projection onto…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong…
Recent efforts to improve the performance of neural network (NN) accelerators that meet today's application requirements have given rise to a new trend of logic-based NN inference relying on fixed-function combinational logic (FFCL). This…
We give an algorithm to compute the local $b$ function. In this algorithm, we use the Mora division algorithm in the ring of differential operators and an approximate division algorithm in the ring of differential operators with power…
A novel algorithm for producing smooth nonlinearities on digital hardware is presented. The non-linearities are inherently quadratic and have both symmetrical and asymmetrical variants. The integer (and fixed point) implementation is highly…
Sorting is a fundamental operation in various applications and a traditional research topic in computer science. Improving the performance of sorting operations can have a significant impact on many application domains. For high-performance…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…