Minimax matrix correction of inconsistent systems of linear algebraic equations with block matrices of coefficients

Journal of Computer and Systems Sciences International

Volumn 45, Issue 5, 2006, Pages 727-737

  Gorelik, V A ^a   Erokhin, V I ^b   Pechenkin, R V ^c  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

^b Borisoglebsk State Pedagogical Institute   (Russian Federation)

^c MOSCOW STATE PEDAGOGICAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINED OPTIMIZATION; CORRECTION OF MATRICES; LINEAR ALGEBRAIC EQUATIONS;

FUNCTIONS; LINEAR ALGEBRA; LINEAR EQUATIONS; LINEAR PROGRAMMING; OPTIMIZATION;

PROBLEM SOLVING;

EID: 33749600960     PISSN: 10642307     EISSN: None     Source Type: Journal    
DOI: 10.1134/S1064230706050066     Document Type: Article

References (13)

1. A. A. Vatolin, "Approximation of Improper Linear Programming Problems in Accordance with Criteria of the Euclidean Norm," Zh. Vychisl. Mat. Mat. Fiz. 24 (12), 1907-1908 (1984).
2. V. A. Gorelik, "Matrix Correction of Linear Programming Problems with an Inconsistent System of Constraints," Zh. Vychisl. Mat. Mat. Fiz. 41 (11), 1697-1705 (2001).
3. I. I. Eremin, V. D. Mazurov, and N. N. Astaf'ev, Improper Problems of Linear and Convex Programming (Nauka, Moscow, 1983) [in Russian].
4. V. I. Erokhin, "The Properties of an Optimal Single-Rank Correction of the Matrices of Coefficients of Inconsistent Nonhomogeneous Linear Models," Diskret. Anal. Issled. Operats., Ser. 2. 9 (1), 33-60 (2002).
5. V. A. Gorelik and V. I. Erokhin, Optimal Matrix Correction of Inconsistent Systems of Linear Algebraic Equations According to the Minimum of the Euclidean Norm (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2004) [in Russian].
6. V. A. Gorelik, V. I. Erokhin, and R. V. Pechenkin, "Optimal Matrix Correction of Inconsistent Systems of Linear Algebraic Equations with Block Matrices of Coefficients," Diskret. Anal. Issled. Operats., Ser. 2 12 (2), 3-22 (2005).
7. V. I. Tsurkov, Decomposition in Large-Scale Problems (Nauka, Moscow, 1981) [in Russian].
8. R. Horn and Ch. Johnson, Ch., Matrix Analysis (Cambridge University Press, Cambridge, 1986; Mir, Moscow, 1989).
9. Kh. D. Ikramov, Problem Book in Linear Algebra (Nauka, Moscow, 1975) [in Russian].
10. A. N. Tikhonov, On Normal Solutions to Approximate Systems of Linear Algebraic Equations, Dokl. AN SSSR 254 (3), 549-554 (1980).
11. V. A. Gorelik and R. R. Ibatulin, "A Correction of the System of Constraints of a Linear Programming Problem with the Minimax Criterion," in Simulation, Decomposition, and Optimization of Complex Dynamic Processes (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2001), pp. 89-107 [in Russian].
12. A. E. Albert, Regression and the Moore-Penrose Pseudoinverse (Academic Press, New York, 1972; Nauka, Moscow, 1977).
13. F. R. Gantmakher, The Theory of Matrices (Nauka, Moscow, 1988) [in Russian].