"244918" . . "A Residual Existence Theorem for Linear Equations"@en . . "RIV/67985807:_____/10:00332762!RIV10-AV0-67985807" . . . . "A Residual Existence Theorem for Linear Equations" . . "DE - Spolkov\u00E1 republika N\u011Bmecko" . . . "Optimization Letters" . . "A residual existence theorem for linear equations is proved: if $A\\in\\Rmn$, $b\\in\\Rm$ and if $X$ is a finite subset of $\\Rn$ satisfying $\\max_{x\\in X}p^T(Ax-b)\\geq 0$ for each $p\\in\\Rm$, then the system of linear equations $Ax=b$ has a solution in the convex hull of $X$. An application of this result to unique solvability of the absolute value equation $Ax+B|x|=b$ is given."@en . . "P(GA201/09/1957), P(GC201/08/J020), Z(AV0Z10300504)" . "A residual existence theorem for linear equations is proved: if $A\\in\\Rmn$, $b\\in\\Rm$ and if $X$ is a finite subset of $\\Rn$ satisfying $\\max_{x\\in X}p^T(Ax-b)\\geq 0$ for each $p\\in\\Rm$, then the system of linear equations $Ax=b$ has a solution in the convex hull of $X$. An application of this result to unique solvability of the absolute value equation $Ax+B|x|=b$ is given." . "2" . "RIV/67985807:_____/10:00332762" . . "4" . . . . . . "4"^^ . . "1"^^ . "[19807E679E9F]" . . "A Residual Existence Theorem for Linear Equations"@en . . "Rohn, Ji\u0159\u00ED" . "1862-4472" . "A Residual Existence Theorem for Linear Equations" . . "1"^^ . "linear equations; solution; existence; residual; convex hull; absolute value equation"@en . .