• SJSU Singular Matrix Database
• Matrix group: Gaertner
• Click here for a description of the Gaertner group.
• Click here for a list of all matrices
• Click here for a list of all matrix groups

• Matrix: Gaertner/nopoly
• Description: Structuresymmetric Matrix nopoly K. Gaertner ETH Zurich Jan 1998.
• download as a MATLAB mat-file, file size: 138 KB. Use SJget(356) or SJget('Gaertner/nopoly') in MATLAB.
• download in Matrix Market format, file size: 141 KB.
• download in Rutherford/Boeing format, file size: 112 KB.

A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

Routine svds_err, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 10771 to 10774 and associated error bounds. Matrix properties (click for a legend) number of rows 10,774 number of columns 10,774 structural full rank? yes structural rank 10,774 numerical rank 10,773 dimension of the numerical null space 1 numerical rank / min(size(A)) 0.99991 Euclidean norm of A 23.244 calculated singular value # 10773 0.00028689 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 3.8277e-011 calculated singular value # 10774 9.8596e-015 gap in the singular values at the numerical rank: singular value # 10773 / singular value # 10774 2.9097e+010 calculated condition number 2.3575e+015 condest 1.3203e+017 nonzeros 70,842 # of blocks from dmperm 1 # strongly connected comp. 1 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type integer structure symmetric Cholesky candidate? yes positive definite? no

 author K. Gaertner editor F. Grund date 2001 kind undirected weighted graph 2D/3D problem? no SJid 356 UFid 442

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 163,985 167,016 Cholesky flop count 4.6e+006 4.4e+006 nnz(L+U), no partial pivoting 317,196 323,258 nnz(V) for QR, upper bound nnz(L) for LU 222,086 244,670 nnz(R) for QR, upper bound nnz(U) for LU 423,762 462,725

Maintained by Leslie Foster, last updated 24-Apr-2009.

Entries 5 through 14 in the table of matrix properties and the singular
value plot were created using SJsingular code. The other plots
and statistics are produced using utilities from the SuiteSparse package.
Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.