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Structured Sketching for Linear Systems

Johannes J Brust, Michael A Saunders

TL;DR

The document provides a comprehensive guide to the SIAM LaTeX style, detailing how to prepare articles, supplements, and templates with consistent formatting. It covers class options, front matter, cross-referencing, math and theorem environments, tables, figures, algorithms, and sections, along with templates and bibliography conventions. It also documents versioned changes, special modifications, and practices for citations, DOIs, preprints, and software acknowledgments. This guidance enables authors and editors to produce navigable, publication-quality SIAM manuscripts with robust linking, bookmarks, and reproducible templates.

Abstract

For linear systems $Ax=b$ we develop iterative algorithms based on a sketch-and-project approach. By using judicious choices for the sketch, such as the history of residuals, we develop weighting strategies that enable short recursive formulas. The proposed algorithms have a low memory footprint and iteration complexity compared to regular sketch-and-project methods. In a set of numerical experiments the new methods compare well to GMRES, SYMMLQ and state-of-the-art randomized solvers.

Structured Sketching for Linear Systems

TL;DR

The document provides a comprehensive guide to the SIAM LaTeX style, detailing how to prepare articles, supplements, and templates with consistent formatting. It covers class options, front matter, cross-referencing, math and theorem environments, tables, figures, algorithms, and sections, along with templates and bibliography conventions. It also documents versioned changes, special modifications, and practices for citations, DOIs, preprints, and software acknowledgments. This guidance enables authors and editors to produce navigable, publication-quality SIAM manuscripts with robust linking, bookmarks, and reproducible templates.

Abstract

For linear systems we develop iterative algorithms based on a sketch-and-project approach. By using judicious choices for the sketch, such as the history of residuals, we develop weighting strategies that enable short recursive formulas. The proposed algorithms have a low memory footprint and iteration complexity compared to regular sketch-and-project methods. In a set of numerical experiments the new methods compare well to GMRES, SYMMLQ and state-of-the-art randomized solvers.
Paper Structure (29 sections, 2 theorems, 7 equations, 2 figures, 2 tables, 1 algorithm)

This paper contains 29 sections, 2 theorems, 7 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Class options
  3. Front matter
  4. Cross references and hyperlinks
  5. Cleveref
  6. Hyperef
  7. Math and equations
  8. Theorem-like environments
  9. Tables
  10. Figures
  11. Algorithms
  12. Sections
  13. Supplemental material
  14. Template
  15. Bibliography
  16. ...and 14 more sections

Key Result

Theorem 6.1

\newlabelthm:mvt0 Suppose $f$ is a function that is continuous on the closed interval $[a,b]$. and differentiable on the open interval $(a,b)$. Then there exists a number $c$ such that $a < c < b$ and In other words, $f(b)-f(a) = f'(c)(b-a)$.

Figures (2)

  • Figure 1: Example figure using external image files.
  • Figure 2: Example PGFPLOTS figure.

Theorems & Definitions (5)

  • Theorem 6.1: Mean Value Theorem
  • Corollary 6.2
  • Proof 1
  • Claim 6.3
  • Proof 2: Proof of main theorem