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


  • Matrix: Regtools/ursell_200
  • Description: URSELL 200x200 Test problem: integral equation with no square integrable solution.
  • download as a MATLAB mat-file, file size: 53 KB. Use SJget(258) or SJget('Regtools/ursell_200') in MATLAB.
  • download in Matrix Market format, file size: 80 KB.
  • download in Rutherford/Boeing format, file size: 14 KB.

    Regtools/ursell_200

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    Regtools/ursell_200

    Matrix properties (click for a legend)  
    number of rows200
    number of columns200
    structural full rank?yes
    structural rank200
    numerical rank 198
    dimension of the numerical null space2
    numerical rank / min(size(A))0.99
    Euclidean norm of A 0.53621
    calculated singular value # 1983.9644e-014
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.2204e-014
    calculated singular value # 1991.7468e-014
    gap in the singular values at the numerical rank:
    singular value # 198 / singular value # 199
    2.2695
    calculated condition number3.3401e+013
    condest1.8363e+014
    nonzeros40,000
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorUrsell
    editorPer Christian Hansen
    date1974
    kindill-posed problem
    2D/3D problem?no
    SJid258
    UFid-

    Additional fieldssize and type
    bfull 200-by-1

    Notes:

        Constructed by the call [A,b]= ursell(200)                                  
                                                                                    
      where ursell is from Regularization Tools. The description of                 
      ursell from http://www2.imm.dtu.dk/~pch/Regutools/ is:                        
                                                                                    
      [A,b] = ursell(n)                                                             
                                                                                    
      Discretization of a first kind Fredholm integral equation with                
      kernel K and right-hand side g given by                                       
         K(s,t) = 1/(s+t+1) ,  g(s) = 1 ,                                           
      where both integration itervals are [0,1].                                    
                                                                                    
      Note: this integral equation has NO square integrable solution.svals = svd(A);
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))20,100 20,100
    Cholesky flop count2.7e+006 2.7e+006
    nnz(L+U), no partial pivoting40,000 40,000
    nnz(V) for QR, upper bound nnz(L) for LU20,100 20,100
    nnz(R) for QR, upper bound nnz(U) for LU20,100 20,100

    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.