ZLATKO DRMAČ

PROFESSOR OF MATHEMATICS
DEPARTMENT OF MATHEMATICS
UNIVERSITY OF ZAGREB
Address      Research Interest     Projects     Scientific Activities     Teaching     Consulting    
OBAVIJEST: NUMERIČKA ANALIZA 1 (2020-2021, početak nastave)

Address
Department of Mathematics,
Bijenička 30, 10000 Zagreb, CROATIA
Phone: ++385-1-460 5740
Fax: ++385-1-468 0335
Email: drmac@math.hr
Google Scholar profile,
Researcher ID ,
ORCID ID

Previous positions:
2014-2015 Visiting professor at the Department of Mathematics, and visiting scientist at the ICAM at Virginia Tech, Blacksburg, Virginia;
2007-2008 Visiting professor at the Department of Mathematics, and visiting scientist at the ICAM at Virginia Tech, Blacksburg, Virginia;
1998-2007 Assistant, associate and full professor at the Department of Mathematics, University of Zagreb.
1995-1998 Research Associate at the Department of Computer Science, University of Colorado at Boulder Boulder, Colorado, USA;
1991-1994 Wissenschaftlicher Mitarbeiter, FernUniversitaet Hagen, Germany;
1989-1991 Teaching Assistant at the Department of Mathematics, University of Zagreb;
1989 Engineer in INA (mineral oil industry).

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Research Interest
  • Numerical Linear Algebra (SVD, GSVD, eigenvalue problems)
  • Matrix Theory (perturbation theory, spectral problems)
  • Matrix Computations in Signal Processing, Control Theory
  • Model order reducion (POD, DEIM)
  • Numerics of Koopman analysis of complex dynamical systems (DMD)
  • Data Mining (LSI, segmentation)
  • Reliable Numerical Software Development
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Awards
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Associate Editor in
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Current Projects
Completed Projects
  • Quadratic eigenvalue problem in simulation of powertrains; coPI. An industrial research project funded by the AVL.
  • NVIDIA Academic Partnership Program; PI. 2015. Equipment donation, GPU Tesla K40. Funded by NVIDIA.
  • Excellence in research special grant; PI, supported by the Croatian Ministry of Science and Technology.
  • Spectral decompositions-numerical methods and applications; PI, supported by the Croatian Ministry of Science and Technology.
  • Designing highly accurate algorithms for eigenvalue and singular value decompositions; PI, supported by the Volkswagen Science Fundation .
  • Collaborator at ERP (PI for maritime border control/protection methods), a project at the Faculty of Electrical Engineering and Computing (FER).
  • Numerical analysis and matrix theory; PI, supported by the Croatian Ministry of Science and Technology.

Previous research (work with E. Jessup at the University of Colorado at Boulder) supported by the USA Department of Energy, National Science Foundations, Office of Cross Disciplinary Activities, and the Intel corporation.

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Scientific Activities
SCIENTIFIC WORK Show all | Contract all or just click any item for detailed list
  • Papers
    • Z. Drmač, I. Mezić, R. Mohr: Data driven modal decompositions: analysis and enhancements, SIAM Journal on Scientific Computing, 2017, in review. (arXiv preprint)
    • Z. Drmač, A. K. Saibaba: The Discrete Empirical Interpolation Method: canonical structure and formulation in weighted inner product spaces, SIAM Journal on Matrix Analysis and Application, 2017, in revision. (arXiv preprint)
    • Z. Drmač: Algorithm 977: A QR-preconditioned QR SVD method for computing the SVD with high accuracy. ACM Transactions on Mathematical Software, 44, 2017.
    • Z. Drmač, S. Gugercin: A new selection operator for the Discrete Empirical Interpolation Method - improved a priori error bound and extensions, SIAM Journal on Scientific Computing, 38-2 (2016), pp. A631-A648.
    • Z. Drmač, S. Gugercin and C. Beattie: Vector Fitting for matrix-valued rational approximation, SIAM Journal on Scientific Computing, 37-5 (2015), pp. A2346-A2379.
    • Z. Drmač: SVD of Hankel matrices in Vandermonde-Cauchy product form. Electronic Transactions on Numerical Analysis (ETNA), 44 (2015), pp. 593-623.
    • Z. Bujanović, Z. Drmač A new framework for implicit restarting of the Krylov-Schur algorithm, Numerical Linear Algebra with Applications Vol 22., No. 2 (2015), pp 220-232.
    • Z. Drmač, S. Gugercin and C. Beattie: Quadrature-based Vector Fitting for discretized H2 approximation, SIAM Journal on Scientific Computing, 37-2 (2015), pp. A625-A652.
    • Z. Drmač, T. Šikić: On spectral properties of a matrix of specialized roots of Lie algebra sln, Rad HAZU, Matematicke znanosti (Croatian Academy of Sciences and Arts (HAZU)), Vol. 18 (2014) pp 55-72
    • N. Bosner, Z. Bujanović, Z. Drmač: Efficient generalized Hessenberg form and applications, ACM Transactions on Mathematical Software, 39 (2013), 3; 19:1-19:19.
    • Z. Bujanovć, Z. Drmač: A contribution to the theory and practice of the Kogbetliantz method for computing the SVD. BIT Numerical Mathematics, Vol. 52, No. 4 (2012), pp 827-849.
    • C. Beattie, Z. Drmac and S. Gugercin: A note on shifted Hessenberg systems and frequency response computation, ACM Transactions on Mathematical Software, Vol. 38, No. 2, 2011
    • Z. Drmač: A global convergence proof for cyclic Jacobi methods with block rotations, SIAM J. Matrix Analysis Appl., Vol. 31 No. 3 (2009) pp 1329-1350 (LAPACK Working Note 196)
    • N. Bosner and Z. Drmač, Subspace gap residuals for Rayleigh--Ritz approximations, SIAM J. Matrix Anal. Appl., 31 (2009), pp. 54-67
    • Z. Drmač and K. Veselić: New fast and accurate Jacobi SVD algorithm: I., SIAM J. Matrix Anal. Appl., 29 (2008), 1322-1342. (LAPACK Working Note 169)
    • Z. Drmač and K. Veselić: New fast and accurate Jacobi SVD algorithm: II., SIAM J. Matrix Anal. Appl., 29 (2008), 1343-1362. (LAPACK Working Note 170)
    • Z. Drmač and Z. Bujanović, On the failure of rank revealing QR factorization software - a case study, ACM Trans. Math. Softw., 35 (2008), 1-28. (LAPACK Working Note 176)
    • J. Barlow, N. Bosner, Z. Drmač: A new stable bidiagonal reduction algorithm, Lin. Alg. Appl. 397 (2005), 35-84.
    • P. Arbenz and Z. Drmač: On positive semidefinite matrices with known null space, SIAM J. Matrix Anal. Appl. 24 (1) (2002), 132-149.
    • Z. Drmač: New accurate algorithms for singular value decomposition of matrix triplets, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1026-1050.
    • Z. Drmač: On principal angles between subspaces of Euclidean space, SIAM J. Matrix. Anal. Appl., 22 (2000), pp. 173-194. (Technical report CU-CS-838-97, Department of Computer Science, University of Colorado at Boulder.)
    • Z. Drmač and K. Veselić: Approximate eigenvectors as preconditioner, Lin. Alg. Appl., 309 (2000), pp. 191-215.
    • Z. Drmač and E. R. Jessup: On accurate quotient singular value computation in floating-point arithmetic, SIAM J. Matrix. Anal. Appl., 22 (2000), pp. 853-873. (Technical report CU-CS-811-96, Department of Computer Science, University of Colorado at Boulder.)
    • Z. Drmač: A posteriori computation of the singular vectors in a preconditioned Jacobi SVD algorithm, IMA J. Numer. Anal. 19 (1999), pp. 191-213.
    • J. Demmel, M. Gu, S. Eisenstat, I. Slapničar, K. Veselić and Z. Drmač: Computing the singular value decomposition with high relative accuracy, Lin. Alg. Appl., 299 (1999), pp. 21-80. (LAPACK Working Note 119)
    • M. W. Berry, Z. Drmač and E. R. Jessup: Using linear algebra for information retrieval, SIAM Review, Vol. 41, No. 2 (1999), pp. 335-362.
    • Z. Drmač: A tangent algorithm for computing the generalized singular value decomposition, SIAM J. Numer. Anal. 35 (1998), pp. 1804-1832.
    • Z. Drmač: Accurate computation of the product induced singular value decomposition with applications, SIAM J. Numer. Anal. 35 (1998), pp. 1969-1994.
    • Z. Drmač: Implementation of Jacobi rotations for accurate singular value computation in floating-point arithmetic, SIAM J. Sci. Comp., 18 (1997), pp. 1200-1222.
    • Z. Drmač and V. Hari: Relative residual bounds for the eigenvalues of a Hermitian semidefinite matrix, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 21-29.
    • V. Hari and Z. Drmač: On scaled almost diagonal Hermitian matrix pairs, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 1000-1012.
    • Z. Drmač: On relative residual bounds for the eigenvalues of a Hermitian matrix, Lin. Alg. Appl., 244 (1996), pp. 155-163.
    • Z. Drmač: On the condition behaviour in the Jacobi method, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 509-514.
    • Z. Drmač, M. Omladič and K. Veselić: On the perturbation of the Cholesky factorization, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1319-1332.
    • Z. Drmač: Generalized Eigensolutions by Jacobi Methods, (ZAMM), 76, Suppl. 1, (1996), pp. 295-297.
    • Z. Drmač: Accurate singular value computation with the Jacobi method, SVD and Signal Processing III, M. Moonen and B. De Moor (Editors), Elsevier 1995, pp. 107-114.
    • Z. Drmač and K. Veselić: Note on the accuracy of the eigensolution of matrices generated by finite elements, SVD and Signal Processing III, M. Moonen and B. De Moor (Editors), Elsevier 1995, pp. 115-121.
    • Z. Drmač and V. Hari: On the quadratic convergence of the J-symmetric Jacobi method, Numerische Mathematik, 64 (1993), pp. 147-180.
  • Mathematical Software
    • New more robust and reliable xGEQP3 and xGEQPF routines (QR factorization with column pivoting) in LAPACK 3.1 with a new partial column norm updating strategy. This fixes a subtle numerical bug (caused by underestimate of the distance to singularity) dating back to LINPACK that can give completely wrong results.
    • New software for SVD computation (procedures xGESVJ and xGEJSV) with high relative accuracy in LAPACK 3.2.
  • Conferences
    • Closing the gap between fast and accurate SVD methods, plenary talk, Householder meeting XVI, Seven Springs, Pennsylvania, USA, 2005.
    • On the speed of the most accurate SVD algorithm, SIAM Conference on Applied Linear Algebra, Williamsburg, Virginia, USA, 2003.
    • Efficient and acccurate computation of generalized singular value decompositions, SPIE 2001, San Diego, California, USA, 2001.
    • On development of accurate eigensolvers, Internatinal Workshop on Accurate Solution of Eigenvalue Problems, Hagen, Germany 2000.
    • Perturbation theory and iterative symmetric eigensolvers, Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado, USA, 2000.
    • Eigenvalue estimates using Rayleigh quotients of Hermitian matrices, presentation at the 7th International Conference on Operational Research KOI98, Rovinj, Croatia, 1998.
    • Singular vectors as solutions of system of linear equations, Internatinal Workshop on Accurate Solution of Eigenvalue Problems, The Pennsylvania State University, University Park, Pennsylvania, USA, 1998.
    • Backward and forward stability in generalized eigenvalue and singular value computation, SIAM Annual Meeting, Toronto, Canada, 1998.
    • On Accurate Algorithms for Canonical Correlations, Weighted Least Squares and Related Generalized Eigenvalue and Singular Value Decompositions. Presentation at the minisymposium "Recent developments in spectral perturbation theory" organized by Roy Mathias at the Sixth SIAM Conference on Applied Linear Algebra, Snowbird, Utah, USA, 1997.
    • A comparison of parallel linear algebra libraries for the implementation of the product SVD (with E. R. Jessup) presentation at the Sixth SIAM Conference on Applied Linear Algebra, Snowbird, Utah, USA, 1997.
    • On principal angles between subspaces of Euclidean space, Fourth Symposium on Matrix Analysis and Applications, Western Michigan University, Kalamazoo, Michigan, USA, 1997. See .
    • Fast and Accurate Algorithms for PSVD and GSVD, SIAM Annual Meeting, Stanford University, California, USA, 1997.
    • Accurate computation of the product eigenvalue and singular value decompositions with applications to system balancing transformations, First Congress of the Croatian Mathematical Society, Zagreb, Croatia, 1996.
    • Accuracy issues in floating point solution to certain generalized eigenvalue and singular value problems, International Workshop on Accurate Eigensolving and Applications, Split, Croatia, 1996.
    • On stable generalized singular value computation, XIII Householder Symposium on Numerical Algebra, Pontresina, Switzerland, 1996.
    • Stable computation of generalized singular values, Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado, USA, 1996.
    • Relative eigenvalue perturbations of diagonalizable matrices, Third Symposium on Matrix Analysis and Applications, Western Michigan University, Kalamazoo, Michigan, USA 1995.
    • Accurate computation of the cosine-sine decomposition with application to the generalized eigenvalue and singular value decompositions, SIAM Annual Meeting, Charlotte, North Carolina, USA, 1995.
    • Generalized eigensolutions by Jacobi methods, Symposium "Accuracy Issues in Eigenvalue Problems " at the ICIAM 1995, Hamburg, Germany, 1995.
    • Accurate singular value computation by Jacobi method, 3rd International Workshop on SVD and Signal Processing, Leuven, Belgium, 1994.
    • Stoerung der Cholesky-Zerlegung, Geselschaft fuer Angewandte Mathematik und Mechanik, Jahrestagung, Braunschweig, Germany, 1994.
  • Invited Presentations, Seminars
    • Perturbation theory and iterative symmetric eigensolvers, Center for Computational Mathematics, Department of Mathematics, University of Colorado at Denver, Denver, Colorado, USA, 2000.
    • On spectral approximation from a subspace, Lehrgebiet Mathematik, FernUniversitaet Hagen, Germany, 1998.
    • On high relative accuracy in matrix singular value and symmetric eigenvalue problems - from perturbation theory to accurate algorithms, Center for Computational Mathematics, Department of Mathematics, University of Colorado at Denver, Denver, Colorado, USA, 1997.
    • Recent development in accurate floating-point computation of the singular value decomposition of products and quotients of matrices, Department of Computer Science and Engineering, The Pennsylvania State University, State College, Pennsylvania, USA, 1997.
    • Ueber die Berechnung singulaerer und verallgemeinerter singulaerer Werte, Lehrgebiet Mathematik, Universitaet Bielefeld, Germany, 1994.
    • Die a posteriori Abschaetzungen fuer die Eigenwerte Hermitescher Matrizen, Lehrgebiet Mathematik, Universitaet Chemnitz, Germany, 1994.
  • Workshops
    • Multiscale Problems in Science and Technology -- Challenges to Mathematical Analysis and Perspectives, Dubrovnik, Croatia, 2000.
    • Finite Element Circus, Center for Computational Mathematics, University of Colorado at Denver, Colorado, USA, 1998.
    • Level Set Mehods, Stanford University, California, USA, 1997.
    • Linear Algebra for Large Scale and Real-Time Applications, NATO Advanced Study Institute, Leuven, Belgium, 1992.
    • Large Scale Scientific Computation, Universitaet Bielefeld, Germany, 1992.
  • Coauthors
    • Peter Arbenz (Swiss Federal Institute of Technology (ETH), Zuerich, Switzerland)
    • Jesse Barlow (The Pennsylvania State University, State College, PA, USA)
    • Christopher Beattie (Virginia Polytechnic Insitute and State University, Blacksburg, VA, USA)
    • Michael Berry (University of Tennessee, USA)
    • Nela Bosner (University of Zagreb, Zagreb, Croatia)
    • Zvonimir Bujanović (University of Zagreb, Zagreb, Croatia)
    • Jim Demmel (University of California at Berkeley, Berkeley, CA, USA)
    • Stan Eisenstat (Yale University, USA)
    • Ming Gu (University of California)
    • Serkan Gugercin (Virginia Polytechnic Insitute and State University, Blacksburg, VA, USA)
    • Vjeran Hari (University of Zagreb, Croatia)
    • Arvind Krishna Saibaba (Department of Mathematics, North Carolina State University, Raleigh, NC, USA)
    • Elizabeth Jessup (University of Colorado at Boulder, USA)
    • Igor Mezi? ( Department of Mechanical Engineering and Mathematics, University of California, Santa Barbara, CA)
    • Ryan Mohr (AIMdyn, Inc., Santa Barbara, CA, USA)
    • Matjaž Omladič (University of Ljubljana, Slovenia)
    • Ivan Slapničar (University of Split, Croatia)
    • Krešimir Veselić (FernUniversitaet Hagen, Germany)
  • Referee and other Duties
      Referee for the journals
    • SIAM Journal on Matrix Analysis and Applications
    • SIAM Journal on Numerical Analysis
    • SIAM Review
    • Linear Algebra and Its Applications
    • Journal of Parallel and Distributed Computing
      Also,
    • Associate Editor of Glasnik Matemati?ki
    • Guest Editor in SIAM Journal on Matrix Analysis and Applications
    • Managing Editor of Operators and Matrices
      and
    • Referee for the Croatian Ministry of Science and Technology
      and
    • Vice-chair of the Croatian Mathematical Society
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Teaching

Courses (graduates)
  • Numerical Analysis 1 (Fall)
  • Numerical Analysis 2 (Spring)
  • Introduction to data mining (Fall)
  • Mathematical models of search engines (Spring)
  • Introduction to control theory (Fall)
  • Case studies in control (Spring)
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Consulting

For more information and references, please send an email to drmac@math.hr.

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