• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
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  • Matrix: Regtools/foxgood_500
  • Description: FOXGOOD 500x500 Test problem: severely ill-posed problem.
  • download as a MATLAB mat-file, file size: 2 MB. Use SJget(231) or SJget('Regtools/foxgood_500') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.

    Regtools/foxgood_500

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

    Regtools/foxgood_500

    Matrix properties (click for a legend)  
    number of rows500
    number of columns500
    structural full rank?yes
    structural rank500
    numerical rank 29
    dimension of the numerical null space471
    numerical rank / min(size(A))0.058
    Euclidean norm of A 0.81084
    calculated singular value # 295.9864e-014
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    5.5511e-014
    calculated singular value # 302.2322e-014
    gap in the singular values at the numerical rank:
    singular value # 29 / singular value # 30
    2.6819
    calculated condition number3.6134e+019
    condest5.1877e+019
    nonzeros250,000
    # 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

    authorFox and Goodwin
    editorPer Christian Hansen
    date1977
    kindill-posed problem
    2D/3D problem?no
    SJid231
    UFid-

    Additional fieldssize and type
    bfull 500-by-1
    xfull 500-by-1

    Notes:

        Constructed by the call [A,b,x]= foxgood(500)                
                                                                     
      where foxgood is from Regularization Tools. The description of 
      foxgood from http://www2.imm.dtu.dk/~pch/Regutools/ is:        
                                                                     
                        [A,b,x] = foxgood(n)                         
                                                                     
      This is a model problem which does not satisfy the             
      discrete Picard condition for the small singular values.       
      The problem was first used by Fox & Goodwin.                   
    

    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.