Shmuel Winograd

Bio: Shmuel Winograd is an academic researcher from IBM. The author has contributed to research in topics: Error detection and correction & Multiplication. The author has an hindex of 27, co-authored 75 publications receiving 7920 citations.

Matrix multiplication via arithmetic progressions

Abstract: We present a new method for accelerating matrix multiplication asymptotically. This work builds on recent ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product. We make novel use of the Salem-Spencer Theorem, which gives a fairly dense set of integers with no three-term arithmetic progression. Our resulting matrix exponent is 2.376.

On computing the discrete Fourier transform

Abstract: New algorithms for computing the Discrete Fourier Transform of n points are described. For n in the range of a few tens to a few thousands these algorithms use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions.

The Organization of Computations for Uniform Recurrence Equations

Abstract: A set equations in the quantities ai(p), where i = 1, 2, · · ·, m and p ranges over a set R of lattice points in n-space, is called a system of uniform recurrence equations if the following property holds: If p and q are in R and w is an integer n-vector, then ai(p) depends directly on aj(p - w) if and only if ai(q) depends directly on aj(q - w). Finite-difference approximations to systems of partial differential equations typically lead to such recurrence equations. The structure of such a system is specified by a dependence graph G having m vertices, in which the directed edges are labeled with integer n-vectors. For certain choices of the set R, necessary and sufficient conditions on G are given for the existence of a schedule to compute all the quantities ai(p) explicitly from their defining equations. Properties of such schedules, such as the degree to which computation can proceed “in parallel,” are characterized. These characterizations depend on a certain iterative decomposition of a dependence graph into subgraphs. Analogous results concerning implicit schedules are also given.

Arithmetic complexity of computations

Abstract: Three examples General background Product of polynomials FIR filters Product of polynomials modulo a polynomial Cyclic convolution and discrete Fourier transform.

The Design and Analysis of Computer Algorithms

Abstract: From the Publisher: With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter. 0201000296B04062001

The Design and Implementation of FFTW3

Abstract: FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.

Randomized Algorithms

Abstract: For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. This book introduces the basic concepts in the design and analysis of randomized algorithms. The first part of the text presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. Although written primarily as a text for advanced undergraduates and graduate students, this book should also prove invaluable as a reference for professionals and researchers.

The SimpleScalar tool set, version 2.0

Abstract: This document describes release 2.0 of the SimpleScalar tool set, a suite of free, publicly available simulation tools that offer both detailed and high-performance simulation of modern microprocessors. The new release offers more tools and capabilities, precompiled binaries, cleaner interfaces, better documentation, easier installation, improved portability, and higher performance. This paper contains a complete description of the tool set, including retrieval and installation instructions, a description of how to use the tools, a description of the target SimpleScalar architecture, and many details about the internals of the tools and how to customize them. With this guide, the tool set can be brought up and generating results in under an hour (on supported platforms).

Computational Complexity: A Modern Approach

Abstract: This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.