Solution of system of linear equations with large coefficients in the diagonal
Solutions of minus partial ordering equations over von Neumann regular rings
In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.
Solvability classes for core problems in matrix total least squares minimization
Linear matrix approximation problems are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...
Solvability of infinite systems of linear equations
Solving systems of two–sided (max, min)–linear equations
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse.
Sparse recovery with pre-Gaussian random matrices
For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ₁-minimization under the optimal condition m ≥ csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ₁-norm and the outer norm depends on probability distributions.
Su alcuni invarianti numerici associati a sistemi di equazioni lineari in un modulo
System of linear equations
The Drazin inverse through the matrix pencil approach and its application to the study of generalized linear systems with rectangular or square coefficient matrices.
The minimum-norm least-squares solution of a linear system and symmetric rank-one updates.
The principle of truncations in applied probability
Théorème pour la discussion d’un système de équations du premier degré à inconnues
Total Reduction of Linear Systems of Operator Equations With the System Matrix in the Companion Form
Über einen algebraischen Satz, welcher in der Theorie der geometrischen Objekte auftritt
Ueber die Auflösung linearer Gleichungen mit reellen Coefficienten
Дискретные уравнения Винера-Хопфа в -нормированных алгебрах
Методы типа стохастической аппроксимации для решения линейных некорректных задач
О множестве решений линейного уравнения с интервально заданными оператором и правой частью.
О неотрицательном решении системы уравнений с нестрого якобиевой матрицей