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Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…
Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…
Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
Iterative phase retrieval algorithms are widely used in digital optics for their efficiency and simplicity. Conventionally, these algorithms do not consider aberrations as they assume an ideal, aberration-free optical system. Here, we…
By using the Ishikawa iterative algorithm, we approximate the fixed points and the best proximity points of a relatively non expansive mapping. Also, we use the von Neumann sequence to prove the convergence result in a Hilbert space…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
Modern computationally-intensive applications often operate under time constraints, necessitating acceleration methods and distribution of computational workloads across multiple entities. However, the outcome is either achieved within the…
Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
Floating-point computations are quickly finding their way in the design of safety- and mission-critical systems, despite the fact that designing floating-point algorithms is significantly more difficult than designing integer algorithms.…
While Deep Neural Networks (DNNs) push the state-of-the-art in many machine learning applications, they often require millions of expensive floating-point operations for each input classification. This computation overhead limits the…
While interior point methods have been the centerpiece of nonlinear programming tools used in science and engineering, their reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it…
This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…
This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of…
Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both inter-node communications and even more-so in on-node data motion. A new approach to address this limitation is to…
The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…