Some Hypermatrix Algorithms in Linear Algebra

The efficient solution of large linear matrix problems plays a central role in both linear and nonlinear structural analysis. Accordingly, a substantial effort has been allocated for the design of computer software in order to handle standard tasks like the solution of linear equations or eigenreduction.

[1]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[2]  T. Johnsen,et al.  Hypermatrix generalization of the Jacobi- and Eberlein-method for computing eigenvalues and eigenvectors of hermitian or non-hermitian matrices , 1974 .

[3]  Edward G. Coffman,et al.  Organizing matrices and matrix operations for paged memory systems , 1969, Commun. ACM.

[4]  G. Fuchs,et al.  Hypermatrix solution of large sets of symmetric positive-definite linear equations , 1972 .

[5]  Friedrich L. Bauer,et al.  Revised report on the algorithm language ALGOL 60 , 1963, CACM.

[6]  C. L. Morgan,et al.  Continua and Discontinua , 1916 .

[7]  H. Rutishauser Computational aspects of F. L. Bauer's simultaneous iteration method , 1969 .

[8]  John Argyris,et al.  The natural factor formulation of the stiffness for the matrix displacement method , 1975 .

[9]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[10]  P. S. Jensen The Solution of Large Symmetric Eigenproblems by Sectioning , 1972 .

[11]  John R. Roy,et al.  On systems of linear equations of the form AtAx = b error analysis and certain consequences for structural applications , 1974 .

[12]  O. E. Brønlund,et al.  QR-factorization of partitioned matrices: Solution of large systems of linear equations with non-definite coefficient matrices , 1974 .

[13]  P. J. Ebertein,et al.  A Jacobi-Like Method for the Automatic Computation of Eigenvalues and Eigenvectors of an Arbitrary Matrix , 1962 .

[14]  J. G. F. Francis,et al.  The QR Transformation A Unitary Analogue to the LR Transformation - Part 1 , 1961, Comput. J..

[15]  S. Falk Berechnung von Eigenwerten und Eigenvektoren normaler Matrizenpaare durch Ritz‐Iteration , 1973 .

[16]  H. Schwarz The eigenvalue problem (A − λB)x = 0 for symmetric matrices of high order , 1974 .

[17]  Alston S. Householder,et al.  Handbook for Automatic Computation , 1960, Comput. J..

[18]  W. E. Gentleman Least Squares Computations by Givens Transformations Without Square Roots , 1973 .