## Jürgen Garloff |

- Prof. Dr. Jürgen Garloff
- Institut für Angewandte Forschung
- Hochschule für Technik, Wirtschaft und Gestaltung Konstanz / University of Applied Sciences
- Postfach 100543
- D-78405 Konstanz
- Germany
- Phone: +49-7531-206-406 (office)
- +49-7533-934975 (home)
- email: garloff at htwg-konstanz dot de
- URL: http://www-home.htwg-konstanz.de/~garloff/

Jürgen Garloff is a Professor emeritus for Mathematics at the Institute for
Applied Research of the Hochschule für Technik, Wirtschaft und Gestaltung -
University of Applied Sciences in Constance, Germany. He studied sociology, philosophy,
economics, business administration, and mathematics at the Universities of Cologne and
Heidelberg, from where he received his diploma in mathematics under the supervision of
Prof. Romberg. 1976-87 he worked as a research associate at the Institute for Applied
Mathematics of the University of Freiburg i. Br.; there he received his doctorate in
mathematics and the Dr. habil. degree. 1987-89 he held an appointment as research
scientist for computational fluid dynamics in industry. 1989-90 he was a professor for
mathematics and computer science at the University of Applied Sciences in Esslingen. He
is also a professor (apl.) at the Department of Mathematics and Statistics at the
University of Constance. He serves on the editorial board of *Reliable
Computing* and on the advisory board of
*International Journal of Fuzzy Computation and Modeling* and is a member of the
International Linear Algebra Society (ILAS).

*Global Optimization:*use of a new relaxation technique for multivariate polynomials.*Robust Control:*robust stability with emphasis on nonlinear parametric dependencies, development of software.*Matrix Analysis:*focusing on total positivity and sign regularity.*Polynomials*with emphasis on the zero distribution of the Hadamard (i.e., coefficientwise) product of polynomials.*Scientific Computing with Result Verification:*Solution of systems of linear equations with not sharply defined coefficients; solution of systems of algebraic equations; tight enclosures for the range of multivariate polynomials and rational functions with applications in structural mechanics; interpolation of interval-valued data for algebraic and trigonometric polynomials, splines, and exponential sums.

- Mohammad Adm (completed 2016)
- Doaa Al-Saafin
- Fatimah Al-Saafin
- Rola AlSeidi (completed 2020)
- Tareq Hamadneh (completed 2018)
- Andrew Paul Smith (completed 2012)
- Jihad Titi (completed 2019)

1. Optimal Bounds for Interval Interpolation with Polynomials and Functions

2. Investigations on Interval Interpolation (Dissertation), *Freiburger
Intervall-Berichte* __80/5__ (1980) (in German)

3. On the Interval Performance of the Fast Fourier Transformation, *Z. Angew.
Math. Mech.* __60__, T291-T292 (1980) (in German)

4. Totally Nonnegative Interval Matrices, in 'Interval Mathematics 1980', K. Nickel,
Ed., Academic Press*,* New York,London,Toronto, pp. 317-327 (1980)

5. Criteria for Sign Regularity of Sets of Matrices, *Linear Algebra and its
Applications* __44__, 153-160 (1982)

6. Majorization between the Diagonal Elements and the Eigenvalues of an Oscillating
Matrix, *Linear Algebra and its Applications* __47__, 181-184 (1982)

7. Intervals of P-Matrices and Related Matrices, *Linear Algebra and its
Applications* __58__, 33-41 (1984) (with S. Bialas)

8. An Inverse Eigenvalue Problem for Totally Nonnegative Matrices, *Linear and
Multilinear Algebra* __17__, 19-23 (1985)

9.
Convex Combinations of Stable Polynomials, *Journal of the Franklin
Institute* __319__, 373-377 (1985) (with S. Bialas)

10. Stability of Polynomials under Coefficient Perturbation, *IEEE Transactions on
Automatic Control* __AC-30__, 310-313 (1985) (with S. Bialas)

11. On Power-Boundedness of Interval Matrices, *J. of Computational and Applied
Mathematics* __14__, 353-360 (1986)

12. Bounds for the Eigenvalues of the Solution of the Discrete Riccati and Lyapunov
Equations and the Continuous Lyapunov Equation, *International Journal of Control*
__43__, 423-431 (1986)

13. Convergent Bounds
for the Range of Multivariate Polynomials, in 'Interval Mathematics 1985', K.
Nickel, Ed., *Lecture Notes in Computer Science,* vol. 212, pp. 37-56, Springer,
Berlin, Heidelberg, New York (1986)

14. Optimal Inclusion of a Solution Set, *SIAM Journal of Numerical Analysis*
__23__, 217-226 (1986) (with R. Krawczyk)

15. New Integration Formulas which Use Nodes outside the Integration Interval,
*Journal of the Franklin Institute* __321__, 115-126 (1986) (with W. Solak and
Z. Szydelko)

16. Solution of Linear Equations Having a Toeplitz Interval Matrix as Coefficient
Matrix, *Opuscula Mathematica* __2__, 33-45 (1986)

17.
The Spectra of Matrices Having Sums of Principal Minors with Alternating Sign,
*SIAM J. Algebraic and Discrete Methods* __8__, 106-107 (1987) (now: *SIAM J.
Matrix Analysis and Applications*) (with V. Hattenbach)

18. Boundary Implications for Stability Properties: Present Status, in 'Reliability in Computing', R.E. Moore, Ed., Academic Press, Boston, San Diego, New York, pp. 391-402, (1988) (with N.K. Bose)

19. Block Methods for the Solution of Linear Interval Equations, *SIAM J. Matrix
Analysis and Applications* __11__, 89-106 (1990)

20. Stability Test of a Polynomial with Coefficients Depending Polynomially on
Parameters, *Wiss. Zeitschrift TH Leipzig* __15__, 415-419 (1991)

21. An Improved Bernstein Algorithm for Robust Stability and Performance Analysis, Proceedings of the Singapore Intern. Conf. on Intelligent Control and Instrumentation, Singapore, Feb. 18-21, 1992, IEEE, pp. 1204-1210 (1992) (with S. Malan, M. Milanese, and M. Taragna)

22. B^{3} Algorithm for Robust Performance Analysis in Presence of Mixed Parametric
and Dynamic Perturbations, Proceedings of the 31st. Control and Decision Conference,
Tucson, Arizona, USA, Dec. 16-18, 1992, IEEE Control System Society, pp. 128-133 (1992)
(with S. Malan, M. Milanese, and M. Taragna)

23. The Bernstein Algorithm, *Interval Computations* __2__, 154-168 (1993)
(now: *Reliable Computing*)

24. Vertex Implications for Totally Nonnegative Matrices, in 'Total Positivity and its Applications', M. Gasca and C.A. Micchelli, Eds. , Kluwer Acad. Publ., Dordrecht, Boston, London, pp. 103-107 (1996)

25. Preservation of Total Nonnegativity unter the Hadamard Product and Related Topics, in 'Total Positivity and its Applications', M. Gasca and C.A. Micchelli, Eds., Kluwer Acad. Publ., Dordrecht, Boston, London, pp. 97-102 (1996) (with D. G. Wagner)

26.
Hadamard Products of Stable Polynomials Are Stable, *Journal Math. Analysis
and Applications* __202__, 797-809 (1996) (with D.G. Wagner)

27. The Hadamard Factorization of Hurwitz and Schur stable Polynomials, in
'Stability Theory'*,* R. Jeltsch and M. Mansour, Eds., *Internat. Series of
Numerical Mathematics (ISNM)*, vol.121, Birkhäuser Verlag, Boston, Basel,
Berlin, pp. 19-21 (1996) (with B. Shrinivasan)

28. Robustness
Analysis of Polynomials with Polynomial Parameter Dependency Using Bernstein
Expansion, *IEEE Trans. Automat. Control* 43, 425-431 (1998) (with M.
Zettler)

29. Speeding
up an Algorithm for Checking Robust Stability of Polynomials, Proc. 2nd IFAC Symp.
*Robust Control Design*, Cs. Banyasz, Ed., Elsevier Sci., Oxford, pp. 183-188
(1998) (with B. Graf and M. Zettler)

30. Bounds
for the Range of a Bivariate Polynomial over a Triangle, *Reliable Computing*
4, 3-13 (1998) (with R. Hungerbühler)

31. Application of Bernstein Expansion to the Solution of Control Problems,
Proceedings of *MISC'99 - Workshop on Applications of Interval Analysis to Systems
and Control*, J. Vehi and M. A. Sainz, Eds., University of Girona, Girona (Spain),
pp. 421-430 (1999)

32. Robust
Schur Stability of Polynomials with Polynomial Parameter Dependency,
*Multidimensional Systems and Signal Processing* 10, 189-199 (1999) (with B.
Graf)

33. Solving
Strict Polynomial Inequalities by Bernstein Expansion, in *The Use of Symbolic
Methods in Control System Analysis and Design*, N. Munro, Ed., The Institution of
Electrical Engineers (IEE), London, pp. 339-352 (1999) (with B. Graf)

34. Software for Solving Robust Performance Problems Based on Bernstein Expansion,
Proceedings of *2nd NICONET Workshop on Numerical Control Software*, INRIA,
Rocquencourt (France), 3.12.99, pp. 35-39 (1999)

35. Computation
of the Bernstein Coefficients on Subdivided Triangles, *Reliable Computing* 6,
115-121 (2000) (with R. Hungerbühler)

36. Application
of Bernstein Expansion to the Solution of Control Problems, *Reliable
Computing* 6, 303-320 (2000)

37. Special Issue of *Reliable Computing* on Applications to Control, Signals,
and Systems (vol. 6, no. 3, 2000) (Guest Editor jointly with E. Walter)

38. Solution of
Systems of Polynomial Equations by Using Bernstein Expansion, in *Symbolic
Algebraic Methods and Verification Methods*, G. Alefeld, S. Rump, J. Rohn, and T.
Yamamoto, Eds., Springer, pp. 87-97 (2001) (with A. P. Smith)

39. Investigation
of a Subdivision Based Algorithm for Solving Systems of Polynomial Equations,
*Journal of Nonlinear Analysis: Series A Theory and Methods* 47/1, 167-178 (2001)
(with A. P. Smith)

40. Intervals of Totally Nonnegative and Related Matrices, *Proceedings in Applied
Mathematics and Mechanics* 1, 496-497 (2002)

41. Intervals of
Almost Totally Positive Matrices, *Linear Algebra and its Applications* 363,
103-108 (2003)

42. The Bernstein
Expansion and its Applications, *Journal of the American Romanian Academy*
(ARA J.), 2000-2003, No. 25-27, 80-85 (2003) (tutorial paper, MS Word format)

43. Lower Bound
Functions for Polynomials, *Journal of Computational and Applied Mathematics*
157, 207-225 (2003) (with C. Jansson and A. P. Smith)

44. Inclusion
Isotonicity of Convex-Concave Extensions for Polynomials Based on Bernstein
Expansion, *Computing* 70, 111-119 (2003) (with C. Jansson and A. P.
Smith)

45. An Improved
Method for the Computation of Affine Lower Bound Functions for Polynomials,
*Frontiers in Global Optimization*, C. A. Floudas and P. M. Pardalos, Eds., Series
Nonconvex Optimization and Its Applications, Kluwer Academic Publ., Boston, Dordrecht,
New York, London, 135-144 (2004) (with A. P. Smith)

46. Accelerating
Consistency Techniques and Prony's Method for Reliable Parameter Estimation of
Exponential Sums, *Global Optimization and Constraint Satisfaction*, C.
Jermann, A. Neumaier, and D. Sam, Eds., Lecture Notes in Computer Science, No. 3478,
Springer-Verlag, Berlin, Heidelberg, 31-45 (2005) (with L. Granvilliers and A. P.
Smith) (in LNCS, ©
Springer-Verlag)

47. A Comparison
of Methods for the Computation of Affine Lower Bound Functions for Polynomials,
*Global Optimization and Constraint Satisfaction*, C. Jermann, A. Neumaier, and D.
Sam, Eds., Lecture Notes in Computer Science, No. 3478, Springer-Verlag, Berlin,
Heidelberg, 71-85 (2005) (with A. P. Smith) (in LNCS, © Springer-Verlag)

48. Rigorous Affine Lower Bound Functions for Multivariate Polynomials and Their Use
in Global Optimisation, *Proceedings of GO'05 -- International Workshop on Global
Optimization*, Almeria, Spain, 18.-22.09.05, L. G. Casado, I. Garcia, E. M. T.
Hendrix, and B. Toth, Eds., 109-113 (2005) (with A. P. Smith)

49. Parametermengenschätzung bei Exponentialsummen, *horizonte* 27, 8-11,
(2005) (with I. Idriss and A. P. Smith)

50. Guaranteed
Parameter Set Estimation for Exponential Sums: The Three-terms Case, *Reliable
Computing* 13, 351-359 (2007) (with I. Idriss and A. P. Smith)

51. Guaranteed Affine Lower
Bound Functions for Multivariate Polynomials, *Proceedings in Applied Mathematics
and Mechanics (PAMM)* 7, 1022905-1022906 (2007) (with A. P. Smith)

52. Rigorous
Affine Lower Bound Functions for Multivariate Polynomials and their Use in Global
Optimisation, Proceedings of the 1st International Conference on Applied
Operational Research, Tadbir Institute for Operational Research, Systems Design and
Financial Services, *Lecture Notes in Management Science* 1, 199-211 (2008) (with
A. P. Smith)

53. Interval
Gaussian Elimination with Pivot Tightening, *SIAM Journal of Matrix Analysis and
Applications* 30(4), 1761-1772 (2009)

54. Solving
Linear Systems with Polynomial Parameter Dependency in the Reliable Analysis of
Structural Frames, *Proceedings of the 2nd International Conference on
Uncertainty in Structural Dynamics*, 15.-17.06.09, Sheffield, UK, N. Sims and K.
Worden, Eds., 147-156 (2009) (with E. D. Popova and A. P. Smith), extended version
available here

55. Verified
Solution for a Simple Truss Structure with Uncertain Node Locations, *Proceedings
of the 18th International Conference on the Application of Computer Science and
Mathematics in Architecture and Civil Engineering*, 7.-9.07.09, Weimar, Germany, K.
Gürlebeck and C. Könke, Eds. (2009) (with A. P. Smith and H. Werkle)

56. Karl L. E.
Nickel (1924-2009), *Reliable Computing* 14, 61-65 (2010)

57. Pivot
Tightening for the Interval Cholesky Method, *Proc. in Applied Mathematics and
Mechanics (PAMM)* 10, 549-550 (2010)

58. A
Verified Monotonicity-Based Solution of a Simple Finite Element Model with Uncertain
Node Locations, *Proc. in Applied Mathematics and Mechanics (PAMM)* 10,
157-158 (2010) (with A. P. Smith and H. Werkle)

59. Verified
Solution for a Statically Determinate Truss Structure with Uncertain Node
Locations, *Journal of Civil Engineering and Architecture* 4(11), 1-10 (2010)
(with A. P. Smith and H. Werkle)

60. A Method
for the Verified Solution of Finite Element Models with Uncertain Node Locations,
*Applications of Statistics and Probability in Civil Engineering*, M. Faber, J.
Köhler, and K. Nishijima, Eds., CRC Press, Boca Raton, Fl., 506-512 (2011) (with
A. P. Smith and H. Werkle)

61. Pivot Tightening for Some Direct Methods for Solving Systems of Linear Interval
Equations, *Proceedings of the 3rd Conference of Mathematical Sciences (CMS
2011)*, 27.-28.04.11, Zarqa, Jordan, 2137-2156 (2011)

62. Bounds on the
Range of Multivariate Rational Functions, *Proc. in Applied Mathematics and
Mechanics (PAMM)* 12, 649-650 (2012), DOI: 10.1002/pamm.201210313 (with A. Schabert
and A. P. Smith)

63. Pivot Tightening
for Direct Methods for Solving Symmetric Positive Definite Systems of Linear Interval
Equations, *Computing* 94(2-4), 97-107 (2012), DOI:
10.1007/s00607-011-0159-7

64.
Special Issue on the Use of Bernstein Polynomials in Reliable Computing: A Centennial
Anniversary, *Reliable Computing* 17,
Preface, i-vii (2012) (with A. P. Smith)

65. Bounding
the Range of a Rational Function over a Box, *Reliable Computing* 17, 34-39
(2012) (with A. Narkawicz, A. P. Smith, and C. A. Muñoz)

66. Solving
Linear Systems with Polynomial Parameter Dependency with Application to the Verified
Solution of Problems in Structural Mechanics, in *Optimization, Simulation, and
Control*, A. Chinchuluun, P. M. Pardalos, R. Enkhbat, and E. N. Pistikopoulos, Eds.,
Series *Springer Optimization and Its Applications* vol. 76, Springer, 301-318
(2013) (with E. D. Popova and A. P. Smith)

67. Intervals of Totally
Nonnegative Matrices, *Linear Algebra and its Applications*
439, 3796-3806 (2013), DOI: 10.1016/j.laa.2013.10.021 (with M. Adm)

68. Invariance of Total Nonnegativity of a Tridiagonal Matrix under Element-wise Perturbation, Operator and Matrices 8(1), 129-137 (2014) (with M. Adm)

69. Improved Tests and Characterizations of Totally Nonnegative Matrices, Electronic Journal of Linear Algebra 27, 588-610 (2014) (with M. Adm)

70.
Convergence of the Simplicial Rational Bernstein Form, in *Modelling*, Computation and Optimization in Information Systems and
Management Sciences, Le Thi Hoai An, Pham Dinh Tao, and Nguyen Ngoc Thanh, Eds.,
Series Advances in Intelligent Systems and
Computing Vol. 359, Springer, 433-441 (2015) (with J. Titi and T. Hamadneh)

71.
Total Nonnegativity of Matrices Related to Polynomial Roots and Poles of Rational Functions,
*Journal of Mathematical Analysis and Applications* 434(1), 780-797 (2016) (with M. Adm and J. Titi)

72.
A Survey of Classes of Matrices Possessing the Interval Property and Related Properties,
*Reliable Computing* 22, 1-14 (2016) (with M. Adm and J. Titi)

73.
Invariance of Total Positivity of a Matrix under Entry-wise Perturbation and
Completion Problems, in: *A Panorama of Mathematics: Pure and Applied,
Contemporary Mathematics,* vol. 658, Amer. Math. Soc., Providence, RI, pp. 115-126 (2016) (with M. Adm)

74.
Intervals of Special Sign Regular Matrices, *Linear and Multilinear Algebra*
64(7), 1424-1444 (2016), DOI: 10.1080/03081087. (with M. Adm)

75.
Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form, in: *Scientific Computing,
Computer Arithmetic, and Validated Numerics, *M. Nehmeier, J. Wolff von Gudenberg, and W. Tucker (Eds.), Lect.
Notes in Comp. Sci. vol. 9553, Springer, pp. 171-179 (2016) (with T. Hamadneh)

76.
Total Nonnegativity of the Extended Perron Complement, *Linear Algebra and Its Applications* 508, 214-224 (2016) (with M. Adm)

77.
Invariance of Total Nonnegativity of a Matrix under Entry-wise Perturbation and Subdirect Sum of Totally Nonnegative Matrices,
*Linear Algebra and Its Applications* 514, 222-233 (2017) (with M. Adm)

78.
Matrix Methods for the Simplicial Bernstein Representation and for the Evaluation of Multivariate Polynomials,
*Applied Maths. and Computation* 315, 246-258 (2017) (with J. Titi)

79.
Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions,
*Reliable Computing* 25, 24-37 (2017) (with J. Titi)

80. Further Applications of the Cauchon Algorithm to Rank Determination and Bidiagonal Factorization,
*Linear Algebra and Its Applications* 545, 240-255 (2018) (with M. Adm, K. Muhtaseb, A. Ghani, and S. Fallat)

81.
Total Nonnegativity of Finite Hurwitz Matrices and Root Location of Polynomials,
*Journal of Mathematical Analysis and Applications* 467, 148-170 (2018) (with M. Adm and M. Tyaglov)

82. Matrix Methods for the Tensorial Bernstein Form *Applied Mathematics and Computation* 346, 254-271 (2019) (with J. Titi)

83. On the spectral properties of nonsingular matrices that are strictly sign-regular for some order with applications to totally positive discrete-time systems *Journal of Mathematical Analysis and Applications* 474, 524-543 (2019) (with R. AlSeidi and M. Margaliot)

84. Relaxing the nonsingularity assumption for intervals of totally nonnegative matrices, *Electron. J. Linear Algebra* 36, 106-123 (2020) (with M. Adm, K. Al Muhtaseb, and A. A. Ghani)

85. Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue, *Special Matrices* 8, 98-103 (2020) (mit D. AlSaafin)

86. Symbolic-numeric computation of the Bernstein coefficients of a polynomial from those of its partial derivatives and of the product of two polynomials, in: Computer Algebra in Scientific Computing. CASC 2020, F. Boulier, M. England, T.M. Sadykov, E.V. Vorozhtsov (Eds.), Lect. Notes in Comp. Sci. Vol.12291, Springer, Cham, pp. 583-599 (2020) (with J. Titi)

87. Discrete-time *k*-positive linear systems, *IEEE Trans. Autom. Control* 66(1), 399-405 (2021) (with R. AlSeidi and M. Margaliot)

88. Characterization, perturbation, and interval property of certain sign-regular matrices, *Linear Algebra and Its Applications* 612, 146-161 (2021) (with M. Adm)

89. Bounds for the range of a complex polynomial over a rectangular region *Journal of Computational and Applied Mathematics* 391, article 113377 (2021) (with J. Titi)

90. Recognition of matrices which are strictly sign-regular of a given order and a generalization of oscillatory matrices *Operator and Matrices*, 15(2), 729-742 (2021) (with R. AlSeidi)

91. Further matrix classes possessing the interval property, *Reliable Computing* 28, 56-70 (2021) (with D. AlSaafin and M. Adm)

92. Bounding the range of a sum of multivariate rational functions, in: M. Ceberio and V. Kreinovich (eds.), Decision Making under Uncertainty and Constraints, Studies in Systems, Decision and Control 217, Springer Nature, Cham, pp. 239-249 (2023) (with M. Adm, J. Titi, and A. Elgayar)

93. Matrices having a positive determinant and all other minors nonpositive, to appear in Special Matrices (with M. Adm and I. Hassuneh)

94. High accuracy computing with the Cauchon algorithm, *submitted* (with M. Adm and F. Rasheed)

2. Review of
Totally Nonnegative Matrices by Shaun M. Fallat and Charles R. Johnson, *Linear
Algebra and its Applications* 436, 3790-3792 (2012), DOI:
10.1016/j.laa.2011.11.038

2. Interval-Related Talks at the 4th International Conference on Frontiers in Global
Optimization, Santorini, Greece, June 8-12, 2003, *Reliable Computing* 10, 63-70
(2004) (with V. Kreinovich)

1. Collection of Scientific Papers Honouring Professor Dr. Karl Nickel on the Occasion of His 6oth Birthday, 2 volumes with together 638 pages, Institut für Angewandte Mathematik, Universität Freiburg i. B., (1984), joint editor with A. Neumaier, D. Norbert, and A. Schäfer

2. Professor Dr. Mieczyslaw Warmus - an early pioneer of interval computations, in J. Dutkiewicz, Mieczyslaw Warmus Life and Academic Work, Wollongong, Australia, ISBN 0-646-42666-4, pp. 130-131 (2006)

2. Interval Mathematics: A Bibliography, *Freiburger Intervall-Berichte,*
__85/6__ 222 pages (1985)

3. Bibliography on Interval Mathematics, Continuation, *Freiburger
Intervall-Berichte* __87/2__, 1-50 (1987)

The bibliographies nos. 2 and 3 are available under http://www.cs.utep.edu/interval-comp/ under Bibliographies on Interval and Related Methods or directly by ftp://ftp.math.utah.edu/pub/tex/bin/intarith.bib .

Jürgen Garloff, Mohammad Adm: Sign-regular Matrices Having the Interval Property,

Last updated: June 2024

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