6 - Universality for the Toda Algorithm
Published online by Cambridge University Press: 24 October 2025
Summary
As noted in the Introduction, in this chapter we consider running the Toda algorithm only until time T(1), the deflation time with block decomposition k = 1 fixed, when the norm of the off-diagonal elements in the first row, and hence the first column, is O(ϵ)
. Define E(t)=∑n=2N|X1n(t)|2
so that if E(t)=0
then X11(t)
is an eigenvalue of H. Thus, with E(t)
as in (6.1), the halting time (or 1-deflation time) for the Toda algorithm is given by T(1)(H)=inf{t:E(t)≤ϵ2}
.
Information
- Type
- Chapter
- Information
- The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix , pp. 129 - 151Publisher: Cambridge University PressPrint publication year: 2025
Accessibility standard: WCAG 2.2 A
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this chapter
complies with version 2.2 of the
Web Content Accessibility Guidelines
(WCAG), offering more comprehensive accessibility measures for a broad range
of users and meets the basic
(A)
level of WCAG compliance, addressing essential accessibility barriers.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.