• 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_500
  • Description: URSELL 500x500 Test problem: integral equation with no square integrable solution.
  • download as a MATLAB mat-file, file size: 686 KB. Use SJget(259) or SJget('Regtools/ursell_500') in MATLAB.
  • download in Matrix Market format, file size: 464 KB.
  • download in Rutherford/Boeing format, file size: 83 KB.


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


    Matrix properties (click for a legend)  
    number of rows500
    number of columns500
    structural full rank?yes
    structural rank500
    numerical rank 497
    dimension of the numerical null space3
    numerical rank / min(size(A))0.994
    Euclidean norm of A 0.53621
    calculated singular value # 4977.0579e-014
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 4983.245e-014
    gap in the singular values at the numerical rank:
    singular value # 497 / singular value # 498
    calculated condition number3.6412e+013
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    editorPer Christian Hansen
    kindill-posed problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 500-by-1


        Constructed by the call [A,b]= ursell(500)                                  
      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'))125,250 125,250
    Cholesky flop count4.2e+007 4.2e+007
    nnz(L+U), no partial pivoting250,000 250,000
    nnz(V) for QR, upper bound nnz(L) for LU125,250 125,250
    nnz(R) for QR, upper bound nnz(U) for LU125,250 125,250

    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.