• 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/baart_1000
  • Description: BAART 1000x1000 Test problem: Fredholm integral equation of the first kind.
  • download as a MATLAB mat-file, file size: 7 MB. Use SJget(236) or SJget('Regtools/baart_1000') in MATLAB.
  • download in Matrix Market format, file size: 11 MB.
  • download in Rutherford/Boeing format, file size: 9 MB.


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


    Matrix properties (click for a legend)  
    number of rows1,000
    number of columns1,000
    structural full rank?yes
    structural rank1,000
    numerical rank 13
    dimension of the numerical null space987
    numerical rank / min(size(A))0.013
    Euclidean norm of A 3.2287
    calculated singular value # 136.2579e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 143.7232e-013
    gap in the singular values at the numerical rank:
    singular value # 13 / singular value # 14
    calculated condition number2.7584e+018
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 1000-by-1
    xfull 1000-by-1


        Constructed by the call [A,b,x]= baart(1000)                 
      where baart is from Regularization Tools. The description of   
      baart from http://www2.imm.dtu.dk/~pch/Regutools/ is:          
                 [A,b,x] = baart(n)                                  
      Discretization of a first-kind Fredholm integral equation with 
      kernel K and right-hand side g given by                        
         K(s,t) = exp(s*cos(t)) ,  g(s) = 2*sinh(s)/s ,              
      and with integration intervals  sin [0,pi/2] ,  t in [0,pi] .  
      The solution is given by                                       
         f(t) = sin(t) .                                             
      The order n must be even.                                      

    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.