Routine svd from Matlab 22.214.171.1244 (R2008a) used to calculate the singular values.
|Matrix properties (click for a legend)|
|number of rows||500|
|number of columns||500|
|structural full rank?||yes|
|dimension of the numerical null space||480|
|numerical rank / min(size(A))||0.04|
|Euclidean norm of A||2.9933|
|calculated singular value # 20||6.9264e-013|
| numerical rank defined using a tolerance |
|calculated singular value # 21||2.9771e-015|
| gap in the singular values at the numerical rank: |
singular value # 20 / singular value # 21
|calculated condition number||1.971e+020|
|# 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|
|editor||Per Christian Hansen|
|Additional fields||size and type|
Constructed by the call [A,b,x]= shaw(500) where shaw is from Regularization Tools. The description of shaw from http://www2.imm.dtu.dk/~pch/Regutools/ is: [A,b,x] = shaw(n) Discretization of a first kind Fredholm integral equation with [-pi/2,pi/2] as both integration intervals. The kernel K and the solution f, which are given by K(s,t) = (cos(s) + cos(t))*(sin(u)/u)^2 u = pi*(sin(s) + sin(t)) f(t) = a1*exp(-c1*(t - t1)^2) + a2*exp(-c2*(t - t2)^2) , are discretized by simple quadrature to produce A and x. Then the discrete right-hand b side is produced as b = A*x. The order n must be even.
|Cholesky flop count||4.2e+007||4.2e+007|
|nnz(L+U), no partial pivoting||250,000||250,000|
|nnz(V) for QR, upper bound nnz(L) for LU||125,250||125,250|
|nnz(R) for QR, upper bound nnz(U) for LU||125,250||125,250|
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.