Associate Professor Anatoli Torokhti

• Undergraduate and graduate courses in Mathematics and related areas including: Numerical Methods, Probability and Statistics, Differential Equations, Applied Analysis, Nonlinear System Theory.

• Computational Mathematics and Mathematical Modeling
• Theoretical Foundations in Applied Analysis
• Mathematical Data Processing
• Statistics
• Numerical Methods for Differential and Integral Equations

Book

A. Torokhti and P. Howlett, Computational Methods for Modelling of Nonlinear Systems, Elsevier, 397 p., 2007.

Recent Book Chapters

P. G. Howlett, C. Pearce and A. P. Torokhti, New Perspectives on Optimal Transforms for Random Vectors, "Optimization: Structure and Applications", (Eds. C. Pearce and E. Hunt), Springer, pp. 245 - 259, 2009.

P. G. Howlett, C. Pearce and A. Torokhti, Constructive Methods for Constrained and Unconstrained Approximation of Mappings in Probability Spaces, "Modern Applied Mathematics", Ed. J.C. Misra, Narosa, New Delhi, pp. 83 – 129, 2005.

A. P. Torokhti, P. G. Howlett and C. E. M. Pearce, Optimal Nonlinear Transforms with Variable Structure, Mathematical Research, Ed. G. S. Osipenko, 9, pp. 421-437, 2003.

Recent Journal Publications

S. Friedland and A. P. Torokhti, Generalized rank-constrained matrix approximations, SIAM J. Matrix Anal. Appl., 29, issue 2, pp. 656-659, 2007.

A. Torokhti and J. Manton, Generic Weighted Filtering of Stochastic Signals, IEEE Trans. on Signal Processing, (accepted) 2009.

A. Torokhti and S. Miklavcic, Data Compression under Constraints of Causality and Variable Finite Memory, Signal Processing, (accepted) 2009.

A. Torokhti and S. Friedland, Towards theory of generic Principal Component Analysis, J. Multivariate Analysis, 100, 4, pp. 661-669, 2009.

A. Torokhti and P. Howlett, Filtering and Compression for Infinite Sets of Stochastic Signals, Signal Processing, 89, pp. 291-304, 2009.

P. G. Howlett, A. Torokhti and C.E.M. Pearce, Optimal Multilinear Estimation of a Random Vector under Constraints of Causality and Limited Memory, Computational Statistics and Data Analysis, 52 , Issue 2, pp. 869-878, 2007.

P. G. Howlett, A. P. Torokhti and C. E. M. Pearce, A Philosophy for the Modelling of Realistic Non-linear Systems, Proc. of Amer. Math. Soc., 132, 2, pp. 353-363, 2003.

A. Torokhti and P. Howlett, Best approximation of identity mapping: the case of variable memory, J. Approx. Theory, 143, 1, pp. 111-123, 2006.

A. Torokhti and P. Howlett, Towards Best Approximation of Nonlinear Systems: A Case of Models with Memory, J. Numerical Functional Analysis &. Optimization, 27, (5-6), pp. 721-756, 2006.

P. G. Howlett, A. P. Torokhti and C. E. M. Pearce, The modeling and numerical simulation of causal non-linear systems, J. Nonlinear Analysis: Theory, Methods & Applications, 47 (8), pp. 5559-5572, 2001.

A. P. Torokhti, P. G. Howlett and C. Pearce, Method of Hybrid Approximations for Modeling of Multidimensional Nonlinear Systems, J. Multidim. Syst. & Signal Processing, 14, no 4, pp. 397-410, 2003.

A. P. Torokhti and P. G. Howlett, Optimal Transform Formed by a Combination of Nonlinear Operators: The Case of Data Dimensionality Reduction, IEEE Trans. on Signal Processing, 54, 4, pp. 1431-1444, 2006.

A. Torokhti, P. Howlett, C. Pearce, Optimal Mathematical Models for Nonlinear Dynamical Systems, J. Math. & Comp. Model. Dynamic. Syst., 9, no.3, pp. 327--343, 2003.

P. Howlett, C. Pearce and A. Torokhti, On Problems of Best Approximation for Nonlinear Operators, J. Nonlinear Functional Anal. Appl., 6, pp. 351--368, 2001.

A. Torokhti, P. Howlett, C. Pearce, Method of Best Successive Approximations for Nonlinear Operators, J. Comput. Anal. Appl., 5, no. 3, pp. 299--312, 2003.

P. Howlett, C. Pearce and A. Torokhti, On Nonlinear Operator Approximation with Preassigned Accuracy, J. Comput. Anal. Appl., 5, no. 3, pp. 273--298, 2003.

Howlett, P. and Torokhti, A., Weak Interpolation and Approximation of Nonlinear Operators on the Space C([0,1]), J. Numerical Functional Analysis &. Optimization, 19, no. 9 & 10, 1998.

Howlett, P., Torokhti, A., A Methodology for the Constructive Approximation of Nonlinear Operators Defined on Non-Compact Sets, J. Numerical Functional Analysis and Optimization, 18, no. 3/4, pp. 343 - 366, 1997.

A. Torokhti and P. Howlett, Constructing Fixed Rank Optimal Estimators with Method of Recurrent Best Approximations, J. Multivariate Analysis, 86, 2, pp. 293-309, 2003.

A. P. Torokhti, P. G. Howlett and C. Pearce, Optimal Recursive Estimation of Raw Data, Annals of Operations Research, 133, 285-302, 2005.

A. Torokhti and P. Howlett, Method of recurrent best estimators of second degree for optimal filtering of random signals, Signal Processing, 83, 5, pp. 1013 - 1024, 2003.

A. Torokhti and P. Howlett, An Optimal Filter of the Second Order, IEEE Trans. on Signal Processing, 49, No 5, pp. 1044--1048, 2001.

P. Howlett, C. Pearce and A. Torokhti, An optimal linear filter for random signals with realisations in Hilbert Space, ANZIAM Journal, 44, pp. 485--500, 2003.

A. Torokhti and P. Howlett, Optimal Fixed Rank Transform of the Second Degree, IEEE Trans. CAS. Part II, Analog & Digital Signal Processing, 48, No 3, pp. 309--315, 2001.

A. P. Torokhti and P. G. Howlett, Best Operator Approximation in Modelling of Nonlinear Systems, IEEE Trans. CAS. Part I, Fundamental theory and applications, 49, no. 12, 1792-1798, 2002.

A. Torokhti and P. Howlett, `On the Best Quadratic Approximation of Nonlinear Systems', IEEE Trans. CAS. Part I, Fundamental theory and applications, 48, No 5, 595--602, 2001.

A. Torokhti, P. Howlett and C. Pearce, `Best Causal Mathematical Models for Nonlinear Systems', IEEE Trans. CAS, Part I, Fundamental theory and applications, 52, No. 5, 1013--1020, 2005.

Recent Research Funding

2009: University of South Australia, Division of Information Technology, Engineering and Environment Research Grant. Project title: "Study of new techniques for modelling of optimal data processing technologies", $8,500 (Chief Investigator: A/Prof. A. Torokhti).

2008: University of South Australia, Division of Information Technology, Engineering and Environment Research Grant. Project title: "New computational techniques for optimal signal/image processing", $10,000 (Chief Investigator: A/Prof. A. Torokhti).

2007-2009: ARC Discovery Grant. Project title: "New perspectives on computing methods for mathematical signal processing", $186,000 Chief Investigator: A/Prof. A. Torokhti. Partner Investigators: Prof. Shmuel Friedland (University of Illinois at Chicago, USA), Prof. Volker Mehrmann (Technical University, Berlin, Germany), A/Prof. Isao Yamada (Tokyo Institute of Technology, Japan).

2007: University of South Australia, Supported Researcher Scheme, $1,500.

2007: University of South Australia, Division of Information Technology, Engineering and Environment Research Grant. Project title: "Towards Theory and Implementation of Generic Principal Component Analysis", $6,709 (Chief Investigator: A/Prof. A. Torokhti).

2006: University of South Australia, Division of Information Technology, Engineering and Environment Research Grant. Project title: "New Approaches to the Solution of the Fokker-Planck equation", $10,000 (Chief Investigator: A/Prof. A. Torokhti).

2006: The Elsevier publishing house grant for the preparation of the book "Computational Methods for Modelling of Nonlinear Systems", $1330.

2005: University of South Australia, Competitive Research Grant. Project title: “Identification and Analysis of Nonlinear Phenomena”, $20,000 (Chief Investigator: A/Prof. A. Torokhti).

2005: University of South Australia, Division of Information Technology, Engineering and Environment Research Grant. Project title: “Constructing Optimal Systems with Given Information Capacity”, $15,000 (Chief Investigator: A/Prof. A. Torokhti).

2004: University of South Australia, Pre-competitive National Competitive Grant. Project title: "Nonlinear transforms and their Applications to Modelling of Dynamical Systems'', $26,000 (Chief Investigator: Dr. A. Torokhti).

2003: University of South Australia, Division of Information Technology, Engineering and Environment Research Grant, Project title: "Optimal estimation of random vectors with the method of partitioned data orthogonalisation'', $15,000 (Chief Investigators: Dr. S. Lucas and Dr. A. Torokhti).

I am able to provide media comment in the following areas of expertise:

Discipline: Mathematics

• Computational Mathematics and Mathematical Modelling
• Theoretical Foundations in Applied Analysis
• Mathematical Data Processing
• Numerical Methods for Differential and Integral Equations