linear equationquasi-undertriangular matricessimplest quasi-undertriangular matricesquasi-standard formel-ementary column tarnsformationsolving theoremWe study an average condition number and an average loss of precision for the solution of linear equations and prove that the average case is strongly ...
Assuming that the solution of the autonomous Riccati differential equation exists for allt \geq 0, we give a necessary and sufficient condition for the solution to be periodic. At the same time, from this condition one can readily obtain the period of this periodic solution. Similar results are...
Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X +A∗X-1A = Q We consider the problem of when the matrix equation X + A∗X-1A = Q has a positive definite solution. Here Q is positive definite. We study both the real......
In order to obtain a physically meaningful solution to the diffusive heat equation for unbounded domains, it is required that (1.4.35)lim|x|→∞∂T∂n(x,t)=0,t>0· Temperature-prescribed boundary conditions are known as Dirichlet type boundary conditions. Sometimes, while constructing appr...
bounded smooth set \(\Omega \) in \(\mathrm{I}\!\mathrm{R}^N,\ N\geqslant 3\), we provide a sufficient condition on the data \(f\) integrable with respect to the distance \(\delta \), to ensure the blow-up of the gradient of the very weak solution for the Dirichlet equation...
THE SOLVABILITY OF THE VARIATIONAL PARABOLIC EQUATION WITH A PERIODIC CONDITION ON THE SOLUTION Anlinear parabolic equation with a periodic condition on the solution solved approximately by the Galerkin's method in the Hilber space. Weak, smooth and g... AS Bondarev 被引量: 0发表: 0年 ...
The author gives necessary and sufficient conditions for the existence of a solution to scalar differential inclusions x ' ∈F(x), x∈. The proof is based on a selection of a single-valued function f(x)∈F(x) which satisfies a necessary and sufficient condition for the existence of a sol...
The dissolving of the fluid at the one side of the barrier will be accompanied by the absorption or evaluation of heat and a corresponding reverse effect when it passes out of the solution at the opposite surface. If Qi is the mean energy per mole of component i transported by the ...
Theorem 4.11 Sufficient Condition for Convex Programming Problem If f(x) is a convex cost function defined on a convex feasible set, then the first-order KKT conditions are necessary as well as sufficient for a global minimum. Thus, if we can show convexity of a problem, any solution of th...
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