• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
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  • Matrix: Regtools/ursell_1000
  • Description: URSELL 1000x1000 Test problem: integral equation with no square integrable solution.
  • download as a MATLAB mat-file, file size: 5 MB. Use SJget(260) or SJget('Regtools/ursell_1000') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 803 KB.

    Regtools/ursell_1000

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

    Regtools/ursell_1000

    Matrix properties (click for a legend)  
    number of rows1,000
    number of columns1,000
    structural full rank?yes
    structural rank1,000
    numerical rank 999
    dimension of the numerical null space1
    numerical rank / min(size(A))0.999
    Euclidean norm of A 0.53621
    calculated singular value # 9991.4779e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.1102e-013
    calculated singular value # 10002.9438e-014
    gap in the singular values at the numerical rank:
    singular value # 999 / singular value # 1000
    5.0205
    calculated condition number1.8215e+013
    condest1.1471e+014
    nonzeros1,000,000
    # 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
    SJid260
    UFid-

    Additional fieldssize and type
    bfull 1000-by-1

    Notes:

        Constructed by the call [A,b]= ursell(1000)                                 
                                                                                    
      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'))500,500 500,500
    Cholesky flop count3.3e+008 3.3e+008
    nnz(L+U), no partial pivoting1,000,000 1,000,000
    nnz(V) for QR, upper bound nnz(L) for LU500,500 500,500
    nnz(R) for QR, upper bound nnz(U) for LU500,500 500,500

    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.