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The Equation |x| - |Ax| = b
Rohn, Jiří
We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant.
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Globální implicitní funkce
Rohn, Jiří
Tento text pochází z roku 1973 a nebyl dosud zveřejněn. Jeho hlavním výsledkem je věta o existenci a jednoznačnosti globální implicitní funkce v Rn. Tomuto výsledku předchází řada pomocných tvrzení.
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Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.
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Plný tet: 0507335-av1 - Download fulltextPDF
Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?
Rohn, Jiří
We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is generally not valid, and we prove that it becomes true under an additional assumption of positive semide niteness of the midpoint matrix. The proof is constructive.
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Plný tet: 0505752-av1 - Download fulltextPDF
Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství
Rohn, Jiří
V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. Bouška, J. Rohn a B. Kalendovský).
Absolute Value Mapping
Rohn, Jiří
We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for each right-hand side.
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Overdetermined Absolute Value Equations
Rohn, Jiří
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.
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Plný tet: 0503902-v1 - Download fulltextPDF
Interval Matrices: Regularity Yields Singularity
Rohn, Jiří
It is proved that regularity of an interval matrix implies singularity of two related interval matrices.
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Plný tet: v1239-16 - Download fulltextPDF
Report on the Last Work by Dr. Erich Nuding
Rohn, Jiří
This is a facsimile copy of a 1994 report on the unpublished last paper by Dr. Erich Nuding. It is being made public here in the hope that even after twenty-two years it may be of interest for researchers working in the area of interval computations because of the intriguing concept of the "fourth modality" which has not been rediscovered during a quarter of century which has elapsed since its original formulation.
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Plný tet: v1235-16 - Download fulltextPDF
A Hybrid Method for Solving Absolute Value Equations
Rohn, Jiří
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Plný tet: v1223-14 - Download fulltextPDF

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