JGD_Trefethen/Trefethen_700
Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
| Name |
Trefethen_700 |
| Group |
JGD_Trefethen |
| Matrix ID |
2210 |
|
Num Rows
|
700 |
|
Num Cols
|
700 |
|
Nonzeros
|
12,654 |
|
Pattern Entries
|
12,654 |
|
Kind
|
Combinatorial Problem |
|
Symmetric
|
Yes |
|
Date
|
2008 |
|
Author
|
N. Trefethen |
|
Editor
|
J.-G. Dumas |
| Structural Rank |
700 |
| Structural Rank Full |
true |
|
Num Dmperm Blocks
|
1 |
|
Strongly Connect Components
|
1 |
|
Num Explicit Zeros
|
0 |
|
Pattern Symmetry
|
100% |
|
Numeric Symmetry
|
100% |
|
Cholesky Candidate
|
yes |
|
Positive Definite
|
yes |
|
Type
|
integer |
| SVD Statistics |
| Matrix Norm |
5.279287e+03 |
| Minimum Singular Value |
1.120774e+00 |
| Condition Number |
4.710395e+03
|
| Rank |
700 |
| sprank(A)-rank(A) |
0 |
| Null Space Dimension |
0 |
| Full Numerical Rank? |
yes |
| Download Singular Values |
MATLAB
|
| Download |
MATLAB
Rutherford Boeing
Matrix Market
|
| Notes |
Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html
Problem 7 of the Hundred-dollar, Hundred-digit Challenge Problems,
SIAM News, vol 35, no. 1.
7. Let A be the 20,000 x 20,000 matrix whose entries are zero
everywhere except for the primes 2, 3, 5, 7, . . . , 224737 along the
main diagonal and the number 1 in all the positions A(i,j) with
|i-j| = 1,2,4,8, . . . ,16384. What is the (1,1) entry of inv(A)?
http://www.siam.org/news/news.php?id=388
Filename in JGD collection: Trefethen/trefethen_700.sms
|
