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A Mehrotra type predictor-corrector interior-point algorithm for linear programming
A new reprojection of the conjugate directions
Óbuda University, Institute of Applied Mathematics, H-1034 Budapest, Bécsi út 96/b, Hungary |
In the paper we apply a Parlett–Kahan's "twice is enough" type algorithm to conjugate directions. We give a lower bound of the digits of precision of the conjugate directions, too.
References:
[1] |
J. Abaffy and E. Spedicato, ABS Projections Algorithms: Mathematical Techniques for Linear and Nonlinear Algebraic Equations, Ellis Horwood Ltd, Chichester, England, 1989. |
[2] |
J. Abaffy,
Reprojection of the conjugate directions in ABS classes Part I, Acta Polytechnica Hungarica, 13 (2016), 7-24.
|
[3] |
J. Abaffy, Reprojection of the Conjugate Directions in the ABS Class: Part Ⅱ, https://aisberg.unibg.it/handle/10446/86246. |
[4] |
H. Golub and C. F. Van Loan, Matrix Computation, North Oxford Academic Press, Oxford, 1983.
![]() ![]() |
[5] |
C. S. Hegedűs,
Reorthogonalization Methods Revisited, Acta Polytechnica Hungarica, 12 (2015), 7-26.
|
[6] |
M. R. Hestenes and E. L. Stiefel,
Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sect, 5 (1952), 409-436.
|
[7] |
B. N. Parlett, The symmetric Eigenvalue Problem, Englewood Cliffs, N. J. Prentice-Hall, 1980. |
show all references
References:
[1] |
J. Abaffy and E. Spedicato, ABS Projections Algorithms: Mathematical Techniques for Linear and Nonlinear Algebraic Equations, Ellis Horwood Ltd, Chichester, England, 1989. |
[2] |
J. Abaffy,
Reprojection of the conjugate directions in ABS classes Part I, Acta Polytechnica Hungarica, 13 (2016), 7-24.
|
[3] |
J. Abaffy, Reprojection of the Conjugate Directions in the ABS Class: Part Ⅱ, https://aisberg.unibg.it/handle/10446/86246. |
[4] |
H. Golub and C. F. Van Loan, Matrix Computation, North Oxford Academic Press, Oxford, 1983.
![]() ![]() |
[5] |
C. S. Hegedűs,
Reorthogonalization Methods Revisited, Acta Polytechnica Hungarica, 12 (2015), 7-26.
|
[6] |
M. R. Hestenes and E. L. Stiefel,
Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sect, 5 (1952), 409-436.
|
[7] |
B. N. Parlett, The symmetric Eigenvalue Problem, Englewood Cliffs, N. J. Prentice-Hall, 1980. |













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