Avoiding Communication in the Lanczos Bidiagonalization Routine and Associated Least Squares QR Solver

Abstract

Communication - the movement of data between levels of memory hierarchy or between processors over a network - is the most expensive operation in terms of both time and energy at all scales of computing. Achieving scalable performance in terms of time and energy thus requires a dramatic shift in the field of algorithmic design. Solvers for sparse linear algebra problems, ubiquitous throughout scientific codes, are often the bottlenecks in application performance due to a low computation/communication ratio. In this paper we develop three potential implementations of communication-avoiding Lanczos bidiagonalization algorithms and discuss their different computational requirements. Based on these new algorithms, we also show how to obtain a communication-avoiding LSQR least squares solver.

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Document Details

Document Type
Technical Report
Publication Date
Apr 12, 2015
Accession Number
ADA624905

Entities

People

  • Erin Carson

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Mathematics
  • Arithmetic
  • Bandwidth
  • Computational Fluid Dynamics
  • Computations
  • Computer Science
  • Convergence
  • Electrical Engineering
  • Engineering
  • Equations
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Polynomials
  • Sparse Matrix

Readers

  • Distributed Systems and Data Platform Development
  • Linear Algebra
  • Parallel and Distributed Computing.