Related papers: Practically efficient methods for performing bit-r…
An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary ($\mathbb{Z}_2$), modular ternary ($\mathbb{Z}_3$) and…
A matrix can be converted into a doubly stochastic matrix by using two diagonal matrices. And a doubly stochastic matrix can be written as a sum of permutation matrices. In this paper, we describe a method to write a given generic matrix in…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces…
This work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
Virtually indexed and virtually tagged (VIVT) caches are an attractive option for micro-processor level-1 caches, because of their fast response time and because they are cheaper to implement than more complex caches such as…
Fault-tolerant distributed applications require mechanisms to recover data lost via a process failure. On modern cluster systems it is typically impractical to request replacement resources after such a failure. Therefore, applications have…
We present a new method for performing global redistributions of multidimensional arrays essential to parallel fast Fourier (or similar) transforms. Traditional methods use standard all-to-all collective communication of contiguous memory…
With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the…
Recent technological developments have led to big data processing, which resulted in significant computational difficulties when solving large-scale linear systems or inverting matrices. As a result, fast approximate iterative matrix…
Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular,…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of the signals is known and calculated in…
We describe a method for training accurate Transformer machine-translation models to run inference using 8-bit integer (INT8) hardware matrix multipliers, as opposed to the more costly single-precision floating-point (FP32) hardware. Unlike…