The Equation |x|-|Ax|=b.
Technical Report No. 1277, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2020, 6 p.
http://hdl.handle.net/11104/0307902
Globalni implicitni funkce (Global Implicit Funktion (in Czech)).
Technical Report No. 1276, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2020, 35 p.
http://hdl.handle.net/11104/0307900
Generalization of a Theorem on Eigenvalues of Symmetric Matrices.
Technical Report No. 1271, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2019, 3 p.
http://hdl.handle.net/11104/0298342
Rozhodovanl za neurcitosti: Pohled matematika na planovane hospodarstvi (Decision Making Under Uncertainty:
A Mathematician's View of Planned Economy (in Czech)).
Technical Report No. 1269, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2019, 12 p.
http://hdl.handle.net/11104/0297666
Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?
Technical Report No. 1268, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2019, 5 p.
http://hdl.handle.net/11104/0297149
Absolute Value Mapping.
Technical Report No. 1266, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2019, 3 p.
http://hdl.handle.net/11104/0296140
Overdetermined Absolute Value Equations.
Technical Report No. 1265, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2019, 3 p.
http://hdl.handle.net/11104/0295667
Diagonally Singularizable Matrices.
Linear Algebra and Its Applications 555 (2018), 84-91.
https://doi.org/10.1016/j.laa.2018.06.010
J. Rohn and S. P. Shary,
Interval Matrices: Regularity Generates Singularity.
Linear Algebra and Its Applications 540 (2018), 149-159.
https://doi.org/10.1016/j.laa.2017.11.020
A Sufficient Condition for an Interval Matrix to Have Full Column Rank.
Journal of Computational Technologies 22 (2017), 59-66.
http://hdl.handle.net/11104/0271644
Interval Matrices: Regularity Yields Singularity.
Technical Report No. 1239, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2016, 3 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0465642-Interval-Matrices-Regularity-Yields-Singularity/
Report on the Last Work by Dr. Erich Nuding.
Technical Report No. 1235, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2016, 8 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0465641-Report-on-the-Last-Work-by-Dr-Erich-Nuding/
An Explicit Enclosure of the Solution Set of Overdetermined Interval Linear Equations.
Reliable Computing 24 (2017), 1-10.
http://interval.louisiana.edu/reliable-computing-journal/volume-24/reliable-computing-24-pp-001-010.pdf
Theoretical Characterization of Enclosures.
Reliable Computing 21 (2016), 140-145.
http://interval.louisiana.edu/reliable-computing-journal/volume-21/reliable-computing-21-pp-140-145.pdf
M. Hladik and J. Rohn,
Radii of Solvability and Unsolvability of Linear Systems.
Linear Algebra and Its Applications 503 (2016), 120-134.
http://www.sciencedirect.com/science/article/pii/S0024379516300374
The Solution Set of Interval Linear Equations is Homeomorphic to
the Unit Cube: An Explicit Construction.
Reliable Computing 21 (2015), 25-34.
http://interval.louisiana.edu/reliable-computing-journal/volume-21/reliable-computing-21-pp-025-034.pdf
Verification of Linear (In)Dependence in Finite Precision Arithmetic.
Mathematics in Computer Science 8 (2014), 323-328.
http://dx.doi.org/10.1007/s11786-014-0196-7
A Hybrid Method for Solving Absolute Value Equations.
Technical Report No. 1223, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2014, 3 p.
http://hdl.handle.net/11104/0233892
A New Proof of the Hansen-Bliek-Rohn Optimality Result.
Technical Report No. 1212, Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 2014, 6 p.
http://www.library.sk/arl-cav/sk/detail-cav_un_epca-0427095-A-New-Proof-of-the-HansenBliekRohn-Optimality-Result/
Explicit Form of Matrices $Q_z$ for an Interval Matrix with Unit Midpoint.
Technical Report No. 1206, Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 2014, 5 p.
http://www.library.sk/arl-cav/sk/detail-cav_un_epca-0425451-/
A Reduction Theorem for Absolute Value Equations.
Technical Report No. 1204, Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 2014, 7 p.
http://www.library.sk/arl-cav/sk/detail-cav_un_epca-0425071-/
A Class of Explicitly Solvable Absolute Value Equations.
Technical Report No. 1202, Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 2014, 4 p.
http://www.library.sk/arl-cav/sk/detail-cav_un_epca-0424937-/
A Two-Matrix Alternative.
Electronic Journal of Linear Algebra 26 (2013), 836-841.
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol26_pp836-841.pdf
A Triple Sufficient Condition for Regularity of Interval Matrices.
Technical Report No. 1185, Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 2013, 6 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0394027-A-Triple-Sufficient-Condition-for-Regularity-of-Interval-Matrices/
A Farkas-Type Theorem for Interval Linear Inequalities.
Optimization Letters 8 (2014), 1591-1598.
http://dx.doi.org/10.1007/s11590-013-0675-9
A Bendixson-Type Theorem for Eigenvalues of Interval Matrices.
Technical Report No. 1184, Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 2013, 3 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0394026-A-BendixsonType-Theorem-for-Eigenvalues-of-Interval-Matrices/
J. Rohn, V. Hooshyarbakhsh and R. Farhadsefat,
An Iterative Method for Solving Absolute Value Equations and Sufficient Conditions
for Unique Solvability. Optimization Letters 8 (2014), 35-44.
http://dx.doi.org/10.1007/s11590-012-0560-y
Letter to the Editor.
Linear and Multilinear Algebra 61 (2013), 697-698.
http://dx.doi.org/10.1080/03081087.2012.698617
A Manual of Results on Interval Linear Problems.
Technical Report No. 1164, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 307 p.
http://www.library.sk/i2/i2.entry.cls?ictx=cav&language=1&op=detail&idx=cav_un_epca*0381706
A Handbook of Results on Interval Linear Problems.
Technical Report No. 1163, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 75 p.
http://www.library.sk/i2/i2.entry.cls?ictx=cav&language=1&op=detail&idx=cav_un_epca*0381680
$(Z,z)$-Solutions.
Technical Report No. 1159, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 3 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0376555-Z-zSolutions/
Theoretical Characterization of Enclosures.
Technical Report No. 1158, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 4 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0376554-Theoretical-Characterization-of-Enclosures/
Compact Form of the Hansen-Bliek-Rohn Enclosure.
Technical Report No. 1157, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 8 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0376430-Compact-Form-of-the-HansenBliekRohn-Enclosure/
Verification of Linear (In)Dependence in Finite Precision Arithmetic.
Technical Report No. 1156, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 8 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0376315-Verification-of-linear-independence-in-finite-precision-arithmetic/
A New Characterization of the Maximum Cut in a Graph.
Technical Report No. 1155, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 3 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0376316-A-New-Characterization-of-the-Maximum-Cut-in-a-Graph-Dedicated-to-the-memory-of-the-Tibetan-meditat/
Calculus Digest.
Technical Report No. 1154, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 26 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0376294-Calculus-Digest/
An Algorithm for Solving the $P$-Matrix Problem.
Technical Report No. 1150, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 9 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0370921-An-Algorithm-for-Solving-the-PMatrix-Problem/
An Algorithm for Solving the System $-e \leq Ax \leq e$, $\|x\|_1 \geq 1$.
Technical Report No. 1149, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 8 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0370919-An-Algorithm-for-Solving-the-System-e-Ax-e-x1-1/
V. Hooshyarbakhsh, R. Farhadsefat and J. Rohn,
A Not-A-Priori-Exponential Necessary and Sufficient Condition for Regularity of Interval Matrices.
Technical Report No. 1147, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 3 p.
http://www.library.sk/i2/i2.entry.cls?ictx=cav&language=1&op=detail&idx=cav_un_epca*0370147
V. Hooshyarbakhsh, T. Lotfi, R. Farhadsefat and J. Rohn,
An Iterative Method for Solving Absolute Value Equations.
Technical Report No. 1145, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 7 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0370147-A-notaprioriexponential-necessary-and-sufficient-condition-for-regularity-of-interval-matrices/
Verified Singular Value Decomposition.
Technical Report No. 1144, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 4 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0370810-Verified-Singular-Value-Decomposition/
Verified Eigendecomposition.
Technical Report No. 1143, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2012, 5 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0370809-Verified-Eigendecomposition/
R. Farhadsefat, J. Rohn and T. Lotfi, Norms of Interval Matrices.
Technical Report No. 1122, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 12 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0362912-Norms-of-Interval-Matrices/
Verified Solutions of Linear Equations.
Technical Report No. 1121, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 9 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0361449-Verified-Solutions-of-Linear-Equations/
VERSOFT: Examples.
Technical Report No. 1119, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 11 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0361332-VERSOFT-Examples/
VERSOFT: Guide.
Technical Report No. 1118, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 6 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0361331-VERSOFT-Guide/
INTLAB Primer.
Technical Report No. 1117, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 9 p.
https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0361330-INTLAB-Primer/
R. Farhadsefat, T. Lotfi and J. Rohn,
A Note on Regularity and Positive Definiteness of Interval Matrices.
Central European Journal of Mathematics 10 (2012), 322-328.
http://dx.doi.org/10.2478/s11533-011-0118-8
An Algorithm for Solving the Absolute Value Inequality.
Technical Report No. 1107, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 7 p.
http://hdl.handle.net/11104/0197006
Every Two Square Matrices of the Same Size Have Some Solution in Common.
Technical Report No. 1106, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 4 p.
http://hdl.handle.net/11104/0196890
An Algorithm for Solving Basic Interval Linear Problems.
Technical Report No. 1105, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 6 p.
http://hdl.handle.net/11104/0196889
The Hansen-Bliek Optimality Result as a Consequence of the General Theory.
Technical Report No. 1104, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 5 p.
http://hdl.handle.net/11104/0195721
Disproving the $P$-Matrix Property.
Technical Report No. 1111, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 7 p.
http://hdl.handle.net/11104/0194436
A Perturbation Theorem for Linear Equations.
Technical Report No. 1103, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2011, 2 p.
http://hdl.handle.net/11104/0194105
An Algorithm for Finding a Singular Matrix in an Interval Matrix.
Technical Report No. 1087, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2010, 9 p.
http://hdl.handle.net/11104/0190430
On Rump's Characterization of $P$-Matrices.
Optimization Letters 6 (2012), 1017-1020.
http://dx.doi.org/10.1007/s11590-011-0318-y
A Theorem of the Alternatives for the Equation $|Ax|-|B||x|=b$.
Optimization Letters 6 (2012), 585-591.
http://dx.doi.org/10.1007/s11590-011-0284-4
An Algorithm for Computing All Solutions of an Absolute Value Equation.
Optimization Letters 6 (2012), 851-856.
http://dx.doi.org/10.1007/s11590-011-0305-3
A Note on Generating $P$-Matrices.
Optimization Letters 6 (2012), 601-603.
http://dx.doi.org/10.1007/s11590-010-0273-z
An Algorithm for Computing the Hull of the Solution Set of Interval Linear Equations.
Linear Algebra and Its Applications 435 (2011), 193-201.
http://dx.doi.org/10.1016/j.laa.2011.02.021
A General Method for Enclosing Solutions of Interval Linear Equations.
Optimization Letters 6 (2012), 709-717.
http://dx.doi.org/10.1007/s11590-011-0296-0
J. Rohn and R. Farhadsefat,
Inverse Interval Matrix: A Survey.
Electronic Journal of Linear Algebra 22 (2011), 704-719.
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol22_pp704-719.pdf
A Characterization of Strong Regularity of Interval Matrices.
Electronic Journal of Linear Algebra 20 (2010), 717-722.
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol20_pp717-722.pdf
Explicit Inverse of an Interval Matrix with Unit Midpoint.
Electronic Journal of Linear Algebra 22 (2011), 138-150.
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol22_pp138-150.pdf
An Improvement of the Bauer-Skeel Bounds.
Technical Report No. 1065, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2010, 9 p.
http://hdl.handle.net/11104/0182727
An Algorithm for Solving the Absolute Value Equation: An Improvement.
Technical Report No. 1063, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2010, 8 p.
http://hdl.handle.net/11104/0181476
A Residual Existence Theorem for Linear Equations.
Optimization Letters 4 (2010), 287-292.
http://dx.doi.org/10.1007/s11590-009-0160-7
On Unique Solvability of the Absolute Value Equation.
Optimization Letters 3 (2009), 603-606.
http://dx.doi.org/10.1007/s11590-009-0129-6
Forty Necessary and Sufficient Conditions for Regularity of Interval Matrices: A Survey.
Electronic Journal of Linear Algebra 18 (2009), 500-512.
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol18_pp500-512.pdf
An Algorithm for Solving the Absolute Value Equation.
Electronic Journal of Linear Algebra 18 (2009), 589-599.
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol18_pp589-599.pdf
Description of All Solutions of a Linear Complementarity Problem.
Electronic Journal of Linear Algebra 18 (2009), 246-252.
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol18_pp246-252.pdf
VERSOFT: Verification software in MATLAB / INTLAB. Available at http://uivtx.cs.cas.cz/~rohn/matlab
A Handbook of Results on Interval Linear Problems. Internet text available at http://uivtx.cs.cas.cz/~rohn/publist/!handbook.pdf
Letter to the Editor. Reliable Computing 12 (2006), 245-246. http://dx.doi.org/10.1007/s11155-006-7222-7
M. Fiedler, J. Nedoma, J. Ramik, J. Rohn and K. Zimmermann, Linear Optimization Problems with Inexact Data. Springer-Verlag, New York 2006, ISBN 0-387-32697-9 (Contents) (Springer sample pages: Chapter 2, 44 p.)
Regularity of Interval Matrices and Theorems of the Alternatives. Reliable Computing 12 (2006), 99-105. http://dx.doi.org/10.1007/s11155-006-4877-z
How Strong Is Strong Regularity? Reliable Computing 11 (2005), 491-493. http://dx.doi.org/10.1007/s11155-005-0407-7
Perron Vectors of an Irreducible Nonnegative Interval Matrix. Linear and Multilinear Algebra 54 (2006), 399-404. http://dx.doi.org/10.1080/03081080500304710
Nonsingularity, Positive Definiteness, and Positive Invertibility Under Fixed-Point Data Rounding. Applications of Mathematics 52 (2007), 105-115. http://dx.doi.org/10.1007/s10492-007-0005-6
Linearni algebra a optimalizace. Nakladatelstvi Karolinum, Prague 2004, 199 p., ISBN 80-246-0932-0
Problem linearni komplementarity a kvadraticke programovani (strucny ucebni text). Technical Report No. 918, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2004, 12 p.
A Method for Handling Dependent Data in Interval Linear Systems. Technical Report No. 911, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2004, 7 p.
Linear Interval Equations: Midpoint Preconditioning May Produce a 100% Overestimation for Arbitrarily Narrow Data Even in Case $n=4$. Reliable Computing 11 (2005), 129-135. http://dx.doi.org/10.1007/s11155-005-3033-5
Linearni algebra a optimalizace na slidech. Technical Report No. 905, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2004, 456 p. (compressed form, 4 slides per page)
A Normal Form Supplement to the Oettli-Prager Theorem. Reliable Computing 11 (2005), 35-39. http://dx.doi.org/10.1007/s11155-005-5941-9
A Theorem of the Alternatives for the Equation $Ax+B|x|=b$. Linear and Multilinear Algebra 52 (2004), 421-426. http://dx.doi.org/10.1080/0308108042000220686
Prehled nekterych dulezitych vet z teorie matic. Technical Report No. 895, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2003, 48 p.
Solvability of Systems of Linear Interval Equations. SIAM Journal on Matrix Analysis and Applications 25 (2003), 237-245. http://dx.doi.org/10.1137/S0895479801398955
Systems of Interval Linear Equations and Inequalities (Rectangular Case). Technical Report No. 875, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2002, 69 p.
Linearni programovani (strucny ucebni text). Technical Report No. 845, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2001, 24 p.
J. Rohn, S. M. Rump and T. Yamamoto, Preface. Linear Algebra and Its Applications 324 (2001), 1-2
J. Rohn, S. M. Rump and T. Yamamoto (eds.), Special issue on linear algebra in self-validating methods. Linear Algebra and Its Applications 324 (2001), No. 1-3, 236 p.
Symbolic Algebraic Methods and Verification Methods (G. Alefeld, J. Rohn, S. Rump and T. Yamamoto, eds.). Springer-Verlag, Wien 2001, ISBN 3-211-83593-8 (Contents and Introduction)
G. Alefeld, J. Rohn, S. M. Rump and T. Yamamoto (eds.), Symbolic-Algebraic Methods and Verification Methods - Theory and Applications. Dagstuhl-Seminar-Report 260, IBFI, Schloss Dagstuhl, Wadern 2000, 34 p. (Overview)
Computing the Norm $\|A\|_{\infty,1}$ is NP-Hard. Linear and Multilinear Algebra 47 (2000), 195-204. http://dx.doi.org/10.1080/03081080008818644
G. Mayer and J. Rohn, On the Applicability of the Interval Gaussian Algorithm. Reliable Computing 4 (1998), 205-222. http://dx.doi.org/10.1023/A:1009997411503
V. Kreinovich, A. Lakeyev, J. Rohn and P. Kahl, Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer Academic Publishers, Dordrecht 1998, ISBN 0-7923-4865-6 (Contents and Preface)
[98] On Overestimations Produced by the Interval Gaussian
Algorithm. Reliable Computing 3 (1997), 363-368.
http://dx.doi.org/10.1023/A:1009993319560
[97] Bounds on Eigenvalues of Interval Matrices.
Zeitschrift fur Angewandte Mathematik und Mechanik 78 (1998), Supplement 3,
S1049-S1050.
http://dx.doi.org/10.1002/zamm.19980781593
[96] Complexity of Some Linear Problems with Interval
Data. Reliable Computing 3 (1997), 315-323.
http://dx.doi.org/10.1023/A:1009987227018
[95] C. Jansson and J. Rohn, An Algorithm for Checking
Regularity of Interval Matrices. SIAM Journal on Matrix Analysis and
Applications 20 (1999), 756-776.
http://dx.doi.org/10.1137/S0895479896313978
[94] G. Rex and J. Rohn, Sufficient Conditions for Regularity
and Singularity of Interval Matrices. SIAM Journal on Matrix Analysis and
Applications 20 (1998), 437-445.
http://dx.doi.org/10.1137/S0895479896310743
[93] Overestimations in Bounding Solutions of Perturbed
Linear Equations. Linear Algebra and Its Applications 262 (1997), 55-65.
https://doi.org/10.1016/S0024-3795(97)80022-5
[92] Checking Properties of Interval Matrices.
Technical Report No. 686, Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 1996, 36 p.
http://hdl.handle.net/11104/0123221
[91] V. Kreinovich, A. Lakeyev and J. Rohn, Computational
Complexity of Interval Algebraic Problems: Some Are Feasible and Some
Are Computationally Intractable - A Survey. In: Scientific Computing and
Validated Numerics (G. Alefeld, A. Frommer and B. Lang, eds.), Akademie Verlag,
Berlin 1996, 293-306
[90] J. Rohn and G. Rex,
Enclosing Solutions of Linear Equations.
SIAM Journal on Numerical Analysis 35 (1998), 524-539.
http://dx.doi.org/10.1137/S0036142996299423
[89] The Conjecture "P$\neq$NP" and Overestimation in Bounding
Solutions of Perturbed Linear Equations. Technical Report No. 644,
Institute of Computer Science, Academy of Sciences of the Czech Republic,
Prague 1995, 5 p.
http://hdl.handle.net/11104/0123117
[88] Enclosing Solutions of Overdetermined Systems of Linear
Interval Equations. Reliable Computing 2 (1996), 167-171
http://dx.doi.org/10.1007/BF02425920
[87] Linear Programming with Inexact Data is NP-Hard.
Zeitschrift fur Angewandte Mathematik und Mechanik 78 (1998), Supplement 3, S1051-S1052
http://dx.doi.org/10.1002/zamm.19980781594
[86] Validated Solutions of Nonlinear Equations.
Zeitschrift fur Angewandte Mathematik und Mechanik 77 (1997), Supplement 2, S657-S658
http://dx.doi.org/10.1002/zamm.19970771407
[85] Complexity of Solving Linear Interval Equations.
Zeitschrift fur Angewandte Mathematik und Mechanik 76 (1996), Supplement 3, 271-274
http://dx.doi.org/10.1002/zamm.19960761310
[84] Linear Interval Equations: Computing Enclosures with
Bounded Relative Overestimation is NP-Hard. In: Applications of Interval
Computations (R. B. Kearfott and V. Kreinovich, eds.), Kluwer Academic
Publishers, Dordrecht 1996, 81-89
[83] Linear Interval Equations: Computing Sufficiently
Accurate Enclosures is NP-Hard. Technical Report No. 621, Institute of
Computer Science, Academy of Sciences of the Czech Republic, Prague 1995, 7 p.
http://hdl.handle.net/11104/0122704
[82] Validated Solutions of Linear Equations.
Technical Report No. 620, Institute of Computer Science, Academy of Sciences of
the Czech Republic, Prague 1995, 11 p.
http://hdl.handle.net/11104/0122703
[81] NP-Hardness Results for Some Linear and Quadratic
Problems. Technical Report No. 619, Institute of Computer Science, Academy
of Sciences of the Czech Republic, Prague 1995, 11 p.
http://hdl.handle.net/11104/0122691
[80] J. Rohn and G. Rex, Interval $P$-Matrices.
SIAM Journal on Matrix Analysis and Applications 17 (1996), 1020-1024
http://dx.doi.org/10.1137/0617062
[79] NP-Hardness Results for Linear Algebraic Problems
with Interval Data. In: Topics in Validated Computations (J. Herzberger,
ed.), North-Holland, Amsterdam 1994, 463-471
[78] Checking Bounds on Solutions of Linear Interval
Equations is NP-Hard. Linear Algebra and Its Applications 223/224 (1995), 589-596
https://doi.org/10.1016/0024-3795(94)00219-4
[77] A Perturbation Theorem for Linear Equations.
Commentationes Mathematicae Universitatis Carolinae 35 (1994), 213-214
(this is a preliminary announcement; click here for a
proof)
http://dml.cz/handle/10338.dmlcz/118656
[76] G. Rex and J. Rohn, A Note on Checking Regularity of
Interval Matrices. Linear and Multilinear Algebra 39 (1995), 259-262
http://dx.doi.org/10.1080/03081089508818399
[75] An Algorithm for Checking Stability of Symmetric
Interval Matrices. IEEE Transactions on Automatic Control 41 (1996), 133-136
http://dx.doi.org/10.1109/9.481618
[74] Checking Positive Definiteness or Stability of Symmetric
Interval Matrices is NP-Hard. Commentationes Mathematicae Universitatis
Carolinae 35 (1994), 795-797
http://dml.cz/handle/10338.dmlcz/118721
[73] Enclosing Solutions of Linear Interval Equations is
NP-Hard. Computing 53 (1994), 365-368
http://dx.doi.org/10.1007/BF02307386
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