JGD_Trefethen/Trefethen_20000b

Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
Name Trefethen_20000b
Group JGD_Trefethen
Matrix ID 2212
Num Rows 19,999
Num Cols 19,999
Nonzeros 554,435
Pattern Entries 554,435
Kind Combinatorial Problem
Symmetric Yes
Date 2008
Author N. Trefethen
Editor J.-G. Dumas
Structural Rank 19,999
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 2.247372e+05
Minimum Singular Value 2.343285e+00
Condition Number 9.590693e+04
Rank 19,999
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_20000__19999_minor.sms