Markus Hegland

A PARALLEL FINITE ELEMENT SURFACE FITTING ALGORITHM FOR DATA MINING

Publisher: PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO.

Date: 05-2000

DOI: 10.1142/9781848160170_0032

Handling silent data corruption with the sparse grid combination technique

Publisher: Springer International Publishing

Date: 2016

DOI: 10.1007/978-3-319-40528-5_9

Modelling gene regulatory networks using Galerkin techniques based on state space aggregation and sparse grids

Publisher: No publisher found

Date: 2008

DOI: 10.1007/978-3-540-79409-7\_17

A new multivariate spline based on mixed partial derivatives and its finite element approximation

Publisher: Elsevier BV

Date: 09-2014

DOI: 10.1016/J.AML.2013.11.008

Recent developments in the theory and application of the sparse grid combination technique

Publisher: Springer International Publishing

Date: 2016

DOI: 10.1007/978-3-319-40528-5_7

Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities

Publisher: Rocky Mountain Mathematics Consortium

Date: 06-2010

DOI: 10.1216/JIE-2010-22-2-285

Mining the MACHO dataset

Publisher: Elsevier BV

Date: 12-2001

DOI: 10.1016/S0010-4655(01)00307-1

On tractability of approximation in special function spaces

Publisher: Elsevier BV

Date: 02-2013

DOI: 10.1016/J.JCO.2012.10.002

The sparse grid combination technique for computing eigenvalues in linear gyrokinetics

Publisher: Elsevier BV

Date: 2013

DOI: 10.1016/J.PROCS.2013.05.208

Numerical integration of particle orbits in discontinuous fields using VENUS-LEVIS and SPEC

Publisher: Elsevier BV

Date: 02-2022

DOI: 10.1016/J.CPC.2021.108191

Fault tolerant computation with the sparse grid combination technique

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2015

DOI: 10.1137/140964448

Current meter calibration and three-dimensional displacement effects,L’etalonnage de moulinets et les ecoulements tri-dimensionnels qui l’accompagnent

Publisher: Informa UK Limited

Date: 10-1982

DOI: 10.1080/00221688209499473

A self-sorting in-place fast Fouriertransform algorithm suitable for vector and parallelprocessing

Publisher: Springer Science and Business Media LLC

Date: 10-1994

DOI: 10.1007/S002110050074

Fitting multidimensional data using gradient penalties and the sparse grid combination technique

Publisher: Springer Science and Business Media LLC

Date: 10-03-2009

DOI: 10.1007/S00607-009-0027-X

Towards a parallel data mining toolbox

Publisher: IEEE Comput. Soc

Date: 2001

DOI: 10.1109/IPDPS.2001.925141

The combination technique and some generalisations

Publisher: Elsevier BV

Date: 2007

DOI: 10.1016/J.LAA.2006.07.014

Stratified space learning: Reconstructing embedded graphs

Publisher: Modelling and Simulation Society of Australia and New Zealand

Date: 12-2019

DOI: 10.36334/MODSIM.2019.A3.BOKOR

Parallelization of a finite element surface fitting algorithm for data mining

Publisher: No publisher found

Date: 2000

DOI: 10.1142/9781848160170\_0032

Real and complex fast Fourier transforms on the Fujitsu VPP 500

Publisher: Elsevier BV

Date: 06-1996

DOI: 10.1016/0167-8191(96)00015-4

An optimal finite state projection method

Publisher: Elsevier BV

Date: 05-2020

DOI: 10.1016/J.PROCS.2010.04.177

Modelling Gene Regulatory Networks Using Galerkin Techniques Based on State Space Aggregation and Sparse Grids

Publisher: Springer Berlin Heidelberg

Date: 2008

DOI: 10.1007/978-3-540-79409-7_17

A note on error bounds for pseudo skeleton approximations of matrices

Publisher: Elsevier BV

Date: 07-2023

DOI: 10.1016/J.LAA.2023.03.024

Variable Hilbert Scales and Their Interpolation Inequalities with Applications to Tikhonov Regularization

Publisher: Informa UK Limited

Date: 12-1995

DOI: 10.1080/00036819508840400

Resolution enhancement of spectra using differentiation

Publisher: IOP Publishing

Date: 11-04-2005

DOI: 10.1088/0266-5611/21/3/008

Convergence rates in ℓ¹-regularization when the basis is not smooth enough

Publisher: Informa UK Limited

Date: 26-02-2015

DOI: 10.1080/00036811.2014.886106

A stochastic model of gene regulation using the chemical master equation

Publisher: Birkhäuser Boston

Date: 2007

DOI: 10.1007/978-0-8176-4558-8_7

Errors of regularisation under range inclusions using variable Hilbert scales

Publisher: American Institute of Mathematical Sciences (AIMS)

Date: 2011

DOI: 10.3934/IPI.2011.5.619

On the computation of breeding values

Publisher: Springer Berlin Heidelberg

Date: 1990

DOI: 10.1007/3-540-53065-7_103

Data mining techniques

Publisher: Cambridge University Press (CUP)

Date: 05-2001

DOI: 10.1017/S0962492901000058

Abstract: Methods for knowledge discovery in data bases (KDD) have been studied for more than a decade. New methods are required owing to the size and complexity of data collections in administration, business and science. They include procedures for data query and extraction, for data cleaning, data analysis, and methods of knowledge representation. The part of KDD dealing with the analysis of the data has been termed data mining. Common data mining tasks include the induction of association rules, the discovery of functional relationships (classification and regression) and the exploration of groups of similar data objects in clustering. This review provides a discussion of and pointers to efficient algorithms for the common data mining tasks in a mathematical framework. Because of the size and complexity of the data sets, efficient algorithms and often crude approximations play an important role.

Parallelisation of sparse grids for large scale data analysis

Publisher: Cambridge University Press (CUP)

Date: 07-2003

DOI: 10.1017/S1446181100003382

Abstract: Sparse grids are the basis for efficient high dimensional approximation and have recently been applied successfully to predictive modelling. They are spanned by a collection of simpler function spaces represented by regular grids. The sparse grid combination technique prescribes how approximations on a collection of anisotropic grids can be combined to approximate high dimensional functions. In this paper we study the parallelisation of fitting data onto a sparse grid. The computation can be done entirely by fitting partial models on a collection of regular grids. This allows parallelism over the collection of grids. In addition, each of the partial grid fits can be parallelised as well, both in the assembly phase, where parallelism is done over the data, and in the solution stage using traditional parallel solvers for the resulting PDEs. Using a simple timing model we confirm that the most effective methods are obtained when both types of parallelism are used.

Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces

Publisher: Informa UK Limited

Date: 06-05-2014

DOI: 10.1080/00036811.2014.912751

Active tectonics and human survival strategies

Publisher: American Geophysical Union (AGU)

Date: 10-10-1994

DOI: 10.1029/94JB00280

Block jacobi preconditioning of the conjugate gradient method on a vector processor

Publisher: Informa UK Limited

Date: 1992

DOI: 10.1080/00207169208804096

The application of sparse grid quadrature in solving stochastic optimisation problems

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 19-06-2019

DOI: 10.21914/ANZIAMJ.V60I0.14060

Parallel performance of fast wavelet transforms

Publisher: World Scientific Pub Co Pte Lt

Date: 03-2000

DOI: 10.1142/S0129053300000059

A functional strategy for nonlinear functionals

Publisher: Modelling and Simulation Society of Australia and New Zealand

Date: 12-2019

DOI: 10.36334/MODSIM.2019.A3.ANDERSSEN2

Sparse grid quadrature on products of spheres

Publisher: Springer Science and Business Media LLC

Date: 25-04-2015

DOI: 10.1007/S11075-015-9958-9

Numerical computation of least constants for the Sobolev inequality

Publisher: Springer Science and Business Media LLC

Date: 11-1986

DOI: 10.1007/BF01399684

Parallel Interior Point Schemes for Solving Multistage Convex Programming

Publisher: Springer Science and Business Media LLC

Date: 2001

DOI: 10.1023/A:1016098709653

Data mining of administrative claims data for pathology services

Publisher: IEEE Comput. Soc

Date: 2001

DOI: 10.1109/HICSS.2001.926572

Data-mining massive time series astronomical data sets-a case study

Publisher: Springer Berlin Heidelberg

Date: 1998

DOI: 10.1007/3-540-64383-4_43

Dilational interpolatory inequalities

Publisher: American Mathematical Society (AMS)

Date: 05-2011

DOI: 10.1090/S0025-5718-2010-02431-7

Sparse grids and hybrid methods for the chemical master equation

Publisher: Springer Science and Business Media LLC

Date: 06-2008

DOI: 10.1007/S10543-008-0174-Z

Derivative spectroscopy an enhanced role for numerical differentiation

Publisher: Rocky Mountain Mathematics Consortium

Date: 09-2010

DOI: 10.1216/JIE-2010-22-3-355

Adaptive sparse grids

Publisher: Elsevier BV

Date: 05-2002

DOI: 10.1016/J.JCP.2009.01.006

Numerical methods for computing the greatest common divisor of univariate polynomials using floating point arithmetic

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 15-08-2019

DOI: 10.21914/ANZIAMJ.V60I0.14059

Abstract: Computing the greatest common isor (GCD) for two polynomials in floating point arithmetic is computationally challenging and even standard library software might return the result GCD=1 even when the polynomials have a nontrivial GCD. Here we review Euclid's algorithm and test a variant for a class of random polynomials. We find that our variant of Euclid's method often produces an acceptable result. However, close monitoring of the norm of the vector of coefficients of the intermediate polynomials is required. References R. M. Corless, P. M. Gianni, B. M. Trager, and S. M. Watt. The singular value decomposition for polynomial systems. In Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ISSAC '95, pages 195207. ACM, 1995. doi:10.1145/220346.220371. H. J. Stetter. Numerical polynomial algebra. SIAM, 2004. doi:10.1137/1.9780898717976. Z. Zeng. The numerical greatest common isor of univariate polynomials. In Randomization, relaxation, and complexity in polynomial equation solving, volume 556 of Contemp. Math., pages 187217. Amer. Math. Soc., 2011. doi:10.1090/conm/556/11014.

The apriori algorithm---a tutorial

Publisher: No publisher found

Date: 2007

DOI: 10.1142/9789812709066\_0006

Mining taxation data with parallel BMARS

Publisher: Informa UK Limited

Date: 06-2000

DOI: 10.1080/01495730008947349

Sparse grids: A new predictive modelling method for the analysis of geographic data

Publisher: Informa UK Limited

Date: 03-2005

DOI: 10.1080/13658810512331319118

A finite element method for density estimation with Gaussian process priors

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2009

DOI: 10.1137/080736478

Scalable parallel algorithms for surface fitting and data mining

Publisher: Elsevier BV

Date: 06-2001

DOI: 10.1016/S0167-8191(01)00076-X

Old wine in fractal bottles I: Orthogonal expansions on self-referential spaces via fractal transformations

Publisher: Elsevier BV

Date: 10-2016

DOI: 10.1016/J.CHAOS.2016.07.007

A parallel algorithm for the reduction to tridiagonal form for eigendecomposition

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 1999

DOI: 10.1137/S1064827595296719

Approximate maximum a posteriori with Gaussian process priors

Publisher: Springer Science and Business Media LLC

Date: 04-04-2007

DOI: 10.1007/S00365-006-0661-4

On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization

Publisher: Springer Science and Business Media LLC

Date: 12-1991

DOI: 10.1007/BF01385791

Journal of Complexity: Guest Editors' Preface

Publisher: Elsevier BV

Date: 10-2010

DOI: 10.1016/S0885-064X(10)00078-6

Spatially-dimension-adaptive sparse grids for online learning

Publisher: Springer International Publishing

Date: 2016

DOI: 10.1007/978-3-319-28262-6_6

Performance analysis of a cardiac simulation code using IPM

Publisher: ACM

Date: 14-11-2011

DOI: 10.1145/2133173.2133186

Approximation of a thin plate spline smoother using continuous piecewise polynomial functions

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2003

DOI: 10.1137/S0036142901383296

THE APRIORI ALGORITHM – A TUTORIAL

Publisher: WORLD SCIENTIFIC

Date: 10-2007

DOI: 10.1142/9789812709066_0006

Low rank approximation of positive semi-definite symmetric matrices using Gaussian elimination and volume sampling

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 14-11-2021

DOI: 10.21914/ANZIAMJ.V62.16036

Abstract: Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve systems with such a matrix can be very costly. A core idea to reduce computational complexity is to approximate the matrix by one with a low rank. The optimal and well understood choice is based on the eigenvalue decomposition of the matrix. Unfortunately, this is computationally very expensive. Cheaper methods are based on Gaussian elimination but they require pivoting. We show how invariant matrix theory provides explicit error formulas for an averaged error based on volume s ling. The formula leads to ratios of elementary symmetric polynomials on the eigenvalues. We discuss several bounds for the expected norm of the approximation error and include ex les where this expected error norm can be computed exactly. References A. Dax. “On extremum properties of orthogonal quotients matrices”. In: Lin. Alg. Appl. 432.5 (2010), pp. 1234–1257. doi: 10.1016/j.laa.2009.10.034. M. Dereziński and M. W. Mahoney. Determinantal Point Processes in Randomized Numerical Linear Algebra. 2020. url: bs/2005.03185. A. Deshpande, L. Rademacher, S. Vempala, and G. Wang. “Matrix approximation and projective clustering via volume s ling”. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm. SODA ’06. Miami, Florida: Society for Industrial and Applied Mathematics, 2006, pp. 1117–1126. url: oi/abs/10.5555/1109557.1109681. S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. “A theory of pseudoskeleton approximations”. In: Lin. Alg. Appl. 261.1 (1997), pp. 1–21. doi: 10.1016/S0024-3795(96)00301-1. M. W. Mahoney and P. Drineas. “CUR matrix decompositions for improved data analysis”. In: Proc. Nat. Acad. Sci. 106.3 (Jan. 20, 2009), pp. 697–702. doi: 10.1073 nas.0803205106. M. Marcus and L. Lopes. “Inequalities for symmetric functions and Hermitian matrices”. In: Can. J. Math. 9 (1957), pp. 305–312. doi: 10.4153/CJM-1957-037-9.

The combination technique applied to functionals

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 07-02-2022

DOI: 10.21914/ANZIAMJ.V62.16112

Abstract: Functionals related to a solution of a problem, usually modelled by partial differential equations, can be important quantities used to capture features of the problem. For high dimensional problems the computational cost of the functionals can be large since the numerical solution of a high dimensional partial differential equation is usually expensive to compute. We develop a new sparse grid combination technique to reduce the computational cost of such functionals. Our method is based on error splitting models of the functionals. However, it is hard to obtain a concrete error splitting model for complicated approximations. We show the connection between the decay of the surpluses and the error splitting models. By using the connection, we can also apply our combination technique to functionals when we only know their computed surpluses. Numerical experiments are provided to illustrate our idea and test the performance of our method. References A. J. Brizard and T. S. Hahm. Foundations of nonlinear gyrokinetic theory. In: Rev. Mod. Phys. 79.2 (2007), pp. 421–468. doi: 10.1103/RevModPhys.79.421 H.-J. Bungartz and M. Griebel. Sparse grids. In: Acta Numer. 13 (2004), pp. 147–269. doi: 10.1017/S0962492904000182 T. Gerstner and M. Griebel. Numerical integration using sparse grids. In: Numer. Algor. 18 (1998), pp. 209–232. doi: 10.1023/A:1019129717644. M. Griebel, M. Schneider, and C. Zenger. A combination technique for the solution of sparse grid problems. In: Iterative methods in linear algebra: Proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra, 1991. Ed. by P. de Groen and R. Beauwens. North-Holland, Amsterdam, 1992, pp. 263–281. url: iewdoc/summary?doi=10.1.1.33.3530 B. Harding. Fault tolerant computation of hyperbolic partial differential equations with the sparse grid combination technique. PhD thesis. The Australian National University, 2016. url: openresearch-repository.anu.edu.au/bitstream/1885/101226/1/Harding%20Thesis%202016.pdf M. Hegland. Adaptive sparse grids. In: Proceedings of the 10th Computational Techniques and Applications Conference CTAC-2001. Ed. by K. Burrage and R. B. Sidje. Vol. 44. 2003, pp. C335–C353. doi: 10.21914/anziamj.v44i0.685 Gene Development Team F. Jenko et al. The Gyrokinetic Plasma Turbulence Code Gene: User Manual. 2013. url: genecode.org/

A solver for the stochastic master equation applied to gene regulatory networks

Publisher: Elsevier BV

Date: 08-2007

DOI: 10.1016/J.CAM.2006.02.053

Eidgenössische Technische Hochschule Zürich

Location: Switzerland

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Australian National University

Location: Australia

View Organisation

Australian Centre For Genome-Phenome Bioinformatics

Start Date: 2003

End Date: 2010

Funder: Australian Research Council

High-performance Computational Data-mining Techniques For Feature Detection In Complex Time Series From Large-scale, Networked Plasma Experiments

Start Date: 2004

End Date: 2006

Funder: Australian Research Council

Investigation And Development Of Parallel Large Scale Record Linkage Techniques

Start Date: 2004

End Date: 2006

Funder: Australian Research Council

Sparse Grid Approximations And Fitting Using Generalised Combination Techniques

Start Date: 2004

End Date: 2006

Funder: Australian Research Council

EXAHD - An Exa-Scalable Two-Level Sparse Grid Approach For Higher-Dimensional Problems In Plasma Physics And Beyond

Start Date: 2012

End Date: 2006

Funder: German Research Foundation

Solving Inverse Problems With Iterative Regularisation And Convex Penalties

Start Date: 2015

End Date: 2017

Funder: Australian Research Council

ARC Complex Open Systems Research Network

Start Date: 2004

End Date: 2009

Funder: Australian Research Council

Energetically Open Systems Research Network Study

Start Date: 2003

End Date: 2003

Funder: Australian Research Council

(Robust Numerical Solution Of Partial Differential Equations On Petascale Computer Systems With Applications To Tsunami Modelling And Plasma Physics)

Start Date: 2011

End Date: 2014

Funder: Australian Research Council

Improving Australia's Data Mining And Knowledge Discovery Research

Start Date: 2003

End Date: 2003

Funder: Australian Research Council

Australian E-Research Grid

Start Date: 2003

End Date: 2003

Funder: Australian Research Council

ARC Centres Of Excellence - Grant ID: CE0348221

Start Date: 2003

End Date: 12-2010

Amount: $7,260,835.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP0453463

Start Date: 2004

End Date: 12-2007

Amount: $100,668.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0451503

Start Date: 2004

End Date: 12-2007

Amount: $171,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP110200410

Start Date: 07-2011

End Date: 06-2016

Amount: $446,000.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354693

Start Date: 2004

End Date: 12-2004

Amount: $10,000.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354716

Start Date: 12-2003

End Date: 12-2004

Amount: $10,000.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354744

Start Date: 2004

End Date: 06-2006

Amount: $20,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP150102345

Start Date: 2015

End Date: 12-2021

Amount: $225,900.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP130101738

Start Date: 05-2013

End Date: 06-2018

Amount: $330,000.00

Funder: Australian Research Council

Research Networks - Grant ID: RN0460006

Start Date: 07-2004

End Date: 06-2009

Amount: $1,500,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0451960

Start Date: 2004

End Date: 12-2008

Amount: $195,000.00

Funder: Australian Research Council