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  1. 3 Open Mathematics

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  1. 3 Übi E.

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  1. 1 2008

  2. 1 2007

  3. 1 2005

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On stable least squares solution to the system of linear inequalities

100%
Übi E.
Open Mathematics
|
2007
|
tom 5
|
nr 2
373-385
EN
The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable and degenerate problems primarily.
2
Content available remote

A numerically stable least squares solution to the quadratic programming problem

88%
Übi E.
Open Mathematics
|
2008
|
tom 6
|
nr 1
171-178
EN
The strictly convex quadratic programming problem is transformed to the least distance problem - finding the solution of minimum norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method, an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm QPLS requires less storage and solves ill-conditioned problems more precisely. The algorithm is illustrated by some difficult problems.
3
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Exact and stable least squares solution to the linear programming problem

88%
Übi E.
Open Mathematics
|
2005
|
tom 3
|
nr 2
228-241
EN
A linear programming problem is transformed to the finding an element of polyhedron with the minimal norm. According to A. Cline [6], the problem is equivalent to the least squares problem on positive ortant. An orthogonal method for solving the problem is used. This method was presented earlier by the author and it is based on the highly developed least squares technique. First of all, the method is meant for solving unstable and degenerate problems. A new version of the artifical basis method (M-method) is presented. Also, the solving of linear inequality systems is considered.
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