Jürgen Garloff
Jürgen Garloff |
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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).
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. B3 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 .