Number of times this page has been accessed since November 11, 1999:

• The Symmetric Real Eigenvalue Problem
  • Dense Full Matrix
    • The Standard All Eigenvalue Problem
      • HITACHI SR2201 (with MPI) 1024PE, Frank Matrix, Problem Size (the number of eigenvalues) : 60,000, The Present Record 3342 sec. (8/Aug. 1997), Eigenvalue Max Relative Error 0.71*10^-6
      • HITACHI SR8000 (with MPI) 32 Nodes, Frank Matrix, Problem Size (the number of eigenvalues) : 160,000, Record 70389 sec. ( 1174min., 19.6hours) (10/Nov. 1999), Eigenvalue Max Relative Error 0.1011*10^-4
      • HITACHI SR8000/MPP (with MPI) 64 Nodes, Frank Matrix, Problem Size (the number of eigenvalues) : 300,000, The Present Record 164611 sec. ( 2743 min., 45.7 hours) (13/April 2001), Eigenvalue Max Relative Error 0.35515*10^-4
    • The Standard All Eigenvalue and All Eiganvector Problem
      • HITACHI SR2201(with MPI) 64PE, Frank Matrix, Problem Size (the number of eigenvalue and eigenvectors) : 12,000, The Present Record 10859 sec. (31/Jan. 1998), Max Eigenvalue Relative Error 0.847 *10^-8, Eigenvector Orthogonality 0.9518 * 10^-12
      • HITACHI SR2201(with MPI) 64PE, Frank Matrix, Problem Size (the number of eigenvalue and eigenvectors) : 12,000, The Present Record 1100 sec. (31/Jan. 1998), Max Eigenvalue Relative Error 0.847 *10^-8, Eigenvector Orthogonality 0.1974 * 10^-9
    • The generalized All Eigenvalue and All Eiganvector Problem
  • Sparse Matrix
    • Tridiagonal Matrix
      • HITACHI SR11000 8PE (1node), (-1,2,-1) Matrix, Problem Size (the number of eigenvalues) : 80,000, All Eigenvalues and All Eigenvectors, The Present Record 4514 sec. (15 May 2006), The accurary is not verified.
      • HITACHI SR11000 8PE (1node), (-1,2,-1) Matrix, Problem Size (the number of eigenvalues) : 40,000, All Eigenvalues and All Eigenvectors, The Present Record 762 sec. (17 May 2006), Orthogonality = 0.293333240699046581E-009, Sum of residual vectors in 2-norm = 0.138708118434071134E-008, Sum of res. vectors in 2-norm/(N*e*T1)= 39.0428644058091834
• The Non-Symmetric Real Eigenvalue Problem

However, these records may be changed.

• Linear Equation Systems
  • Dense Nonsymmetric Matrices
    • Problem Size : 431,344 (1999) , 2335 sec. (theoretical value), ASCI Blue-Pacific SST, IBM SP 604e, 5808 Processors, According to TOP 500 (November 11, 1999).
  • Sparse Nonsymmetric Matrices (Direct Methods)
    • Problem Size : more 300,000? (1994)
  • Sparse Nonsymmetric Matrices (Itarative Methods)
    • Problem Size: 412,128 (1994?), Conjugate Gradient Method
    • Problem Size: 3,100,000 (1994?), GMRES Method
    • Problem Size: 100,000,000?? , showpiece fluids simulation (mesh size:1024 * 1024 * 1024)
• Eigenvalue Problem
  • Dense Symmetric Standard Eigenvalue Problem
    • As for all eigenvalues and eigenvectors, problem size : 27,000 (1994?).
  • Dense Symmetric Generalized Eigenvalue Problem
    • As for all eigenvalues and eigenvectors, problem size: 39,936 (complex double precision), nealy equal 56,500 (real double precision), 4600 dual-processors of Pentium Pro for the ASCI-Red, by using ScaLAPACK, 2103 sec., 684 GFlops.
  • Dense Nonsymmetric Standard Eigenvalue Problem
    • Problem size : 10,000 (1994?).
  • Sparse Symmetric Standard Eigenvalue Problem
    • As for few eigenvalues and/or eigenvecots, problem size : 10,000,000? (1994?), Davidson Method, Intel Touchstone.
  • Sparse Nonsymmetric Standard Eigenvalue Problem
    • As for few eigenvalues and/or eigenvectors, problem size : 500,000? (1994?), iterative Chebyshev-preconditioned Arnoldi Method.
    • As for max 20 eigenvalues and max 20 eigenvectors, Problem size : 12,800,000 (1998?), 57.69 sec., a diagonal matrix with uniform random elements between 0 and 1 with four of the diagonal elements separated from the rest of the spectrum by adding an additional 1.01 to these elements, number of Ritz values requested is 4, 128 Processors of the Maui HPCC SP2, by using P_ARPACK

If you have greater records, would you mail to me?