Skip to content Skip to navigation

Connexions

You are here: Home » Content » Timing of the Lindsey-Fox Algorithm

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice Digital Scholarship

    This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Factoring Polynomials of High Degree"

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

Also in these lenses

  • UniqU content

    This module is included inLens: UniqU's lens
    By: UniqU, LLCAs a part of collection: "Factoring Polynomials of High Degree"

    Click the "UniqU content" link to see all content selected in this lens.

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.
 

Timing of the Lindsey-Fox Algorithm

Module by: C. Sidney Burrus. E-mail the author

Summary: Timing of the factoring of polynomials with the Lindsey-Fox algorithm.

Timings

A large number of polynomials with random coefficients were factored with the Lindsey-Fox program on a 2.6 MHz Pentium with 1 GB RAM in August 2003. The following table shows the average time required for different polynomial degrees. The first column is the polynomial degree (length minus one), the second column is the time in seconds required by Matlab using "roots", and the third column is the time in seconds using the Lindsey-Fox program "lroots" written in Matlab [14]. The polynomial coefficients were random numbers generated by Matlab.

Table 1
Polynomial Degree Time using roots() Time using lroots()
50 0.004 0.04
100 0.020 0.06
200 0.140 0.10
500 3.110 0.23
1,000 24.750 0.50
2,000 250.740 1.20
5,000 13,891.000 6.34
6,000 "Out of memory" 7.49
10,000 "Out of memory" 21.45
100,000 "Out of memory" 1,769.00
150,000 "Out of memory" 4,822.00
250,000 "Out of memory" 9,875.00
500,000 "Out of memory" 45,574.00
1,000,000 "Out of memory" 353,848.00

In order to better understand the Lindsey-Fox program, the individual times required by the three stages algorithm factoring a 2,080,000 degree random coefficient polynomial on a 3 GHz Pentium with 4 GB RAM (run on 1/6/2006) was measured and is presented in the table below. Note the efficient search stage, the time consuming second stage (which can be easily parallelized), and the moderately demanding third stage which can be partially parallelized and which is not always needed.

Table 2
Operation Time in seconds Time in days Percent of total run time
Grid search 16,692 0.2 3.2%
Polish 295,388 3.4 58.0%
Unfactor & Deflate 196,675 2.3 38.8%

The references for the Lindsey-Fox algorithm can be found here

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks