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Hegland, Markus

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Author ID: hegland.markus Recent zbMATH articles by "Hegland, Markus"
Published as: Hegland, M.; Hegland, Markus
Homepage: http://maths-people.anu.edu.au/~hegland/
External Links: MGP · ORCID
Documents Indexed: 79 Publications since 1986, including 1 Book

Publications by Year

Citations contained in zbMATH

57 Publications have been cited 249 times in 200 Documents Cited by Year
A solver for the stochastic master equation applied to gene regulatory networks. Zbl 1121.65009
Hegland, Markus; Burden, Conrad; Santoso, Lucia; MacNamara, Shev; Booth, Hilary
22
2007
The combination technique and some generalisations. Zbl 1109.65052
Hegland, Markus; Garcke, Jochen; Challis, Vivien
22
2007
Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization. Zbl 0841.65039
Hegland, Markus
22
1995
Adaptive sparse grids. Zbl 1078.65520
Hegland, M.
18
2003
For numerical differentiation, dimensionality can be a blessing! Zbl 0921.65018
Anderssen, Robert S.; Hegland, Markus
17
1999
An optimal order regularization method which does not use additional smoothness assumptions. Zbl 0760.65053
Hegland, Markus
12
1992
Fitting multidimensional data using gradient penalties and the sparse grid combination technique. Zbl 1166.65004
Garcke, Jochen; Hegland, Markus
10
2009
A stable finite difference ansatz for higher order differentiation of non-exact data. Zbl 0918.65017
Anderssen, Bob; de Hoog, Frank; Hegland, Markus
8
1998
The trade-off between regularity and stability in Tikhonov regularization. Zbl 0854.65123
Nair, M. Thamban; Hegland, Markus; Anderssen, Robert S.
7
1997
Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces. Zbl 1311.65054
Hegland, Markus; Jin, Qinian; Wang, Wei
6
2015
On tractability of approximation in special function spaces. Zbl 1255.65042
Hegland, M.; Wasilkowski, G. W.
6
2013
A finite element method for density estimation with Gaussian process priors. Zbl 1211.65007
Griebel, Michael; Hegland, Markus
6
2010
Convergence rates in \(\ell^{1}\)-regularization when the basis is not smooth enough. Zbl 1325.65076
Flemming, Jens; Hegland, Markus
5
2015
Numerics and fractals. Zbl 1305.28015
Barnsley, Michael F.; Hegland, Markus; Massopust, Peter
5
2014
Old wine in fractal bottles. I: Orthogonal expansions on self-referential spaces via fractal transformations. Zbl 1372.28006
Bandt, Christoph; Barnsley, Michael; Hegland, Markus; Vince, Andrew
4
2016
Resolution enhancement of spectra using differentiation. Zbl 1080.65124
Hegland, Markus; Anderssen, Robert S.
4
2005
Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. Zbl 1041.65019
Roberts, Stephen; Hegland, Markus; Altas, Irfan
4
2003
A mollification framework for improperly posed problems. Zbl 0896.65042
Hegland, M.; Anderssen, R. S.
4
1998
Parallelising the finite state projection method. Zbl 1386.65046
Sunkara, Vikram; Hegland, Markus
3
2010
Sparse grids and hybrid methods for the chemical master equation. Zbl 1155.65304
Hegland, Markus; Hellander, Andreas; Lötstedt, Per
3
2008
Finite element thin plate splines in density estimation. Zbl 0977.65003
Hegland, Markus; Hooker, Giles; Roberts, Stephen
3
2000
A parallel solver for generalised additive models. Zbl 0942.62078
Hegland, M.; McIntosh, I.; Turlach, B. A.
3
1999
Finite element thin plate splines for surface fitting. Zbl 1016.74066
Hegland, M.; Roberts, S.; Altas, I.
3
1998
On the stable parallel solution of general narrow banded linear systems. Zbl 0930.65017
Arbenz, Peter; Hegland, Markus
3
1998
Wrap-around partitioning for block bidiagonal linear systems. Zbl 0907.65035
Hegland, Markus; Osborne, Michael R.
3
1998
Numerical computation of least constants for the Sobolev inequality. Zbl 0626.46025
Hegland, M.; Marti, J. T.
3
1986
A stabilised mixed finite element method for thin plate splines based on biorthogonal systems. Zbl 1390.65149
Lamichhane, Bishnu Prasad; Hegland, Markus
2
2012
Errors of regularisation under range inclusions using variable Hilbert scales. Zbl 1252.47009
Hegland, Markus; Hofmann, Bernd
2
2011
On the numerical solution of the chemical master equation with sums of rank one tensors. Zbl 1386.65050
Hegland, Markus; Garcke, Jochen
2
2010
Derivative spectroscopy – an enhanced role for numerical differentiation. Zbl 1205.65130
Anderssen, R. S.; Hegland, M.
2
2010
The total quasi-steady state assumption: its justification by singular perturbation theory and its application to the chemical master equation. Zbl 1359.92129
Khoo, Chin Foon; Hegland, Markus
2
2008
Approximate maximum a posteriori with Gaussian process priors. Zbl 1127.65039
Hegland, Markus
2
2007
Parallelisation of sparse grids for large scale data analysis. Zbl 1104.65009
Garcke, Jochen; Hegland, Markus; Nielsen, Ole
2
2006
Multidimensional smoothing using hyperbolic interpolatory wavelets. Zbl 1065.65007
Hegland, Markus; Nielsen, Ole M.; Shen, Zuowei
2
2004
Additive sparse grid fitting. Zbl 1036.65012
Hegland, Markus
2
2003
Parallel interior point schemes for solving multistage convex programming. Zbl 0993.90093
Hegland, M.; Osborne, M. R.; Sun, J.
2
2001
Parallel performance of fast wavelet transforms. Zbl 0973.65135
Nielsen, Ole Møller; Hegland, Markus
2
2000
Real and complex fast Fourier transforms on the Fujitsu VPP 500. Zbl 0875.68489
Hegland, Markus
2
1996
Spatially-dimension-adaptive sparse grids for online learning. Zbl 1356.68168
Khakhutskyy, Valeriy; Hegland, Markus
1
2016
Sparse grid quadrature on products of spheres. Zbl 1330.65045
Hegland, Markus; Leopardi, Paul
1
2015
Fault tolerant computation with the sparse grid combination technique. Zbl 1320.65206
Harding, Brendan; Hegland, Markus; Larson, Jay; Southern, James
1
2015
Robust solutions to PDEs with multiple grids. Zbl 1316.65109
Harding, Brendan; Hegland, Markus
1
2014
A robust combination technique. Zbl 1390.65158
Harding, Brendan; Hegland, Markus
1
2012
Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities. Zbl 1204.65164
Hegland, Markus
1
2010
Approximating the solution of the chemical master equation by aggregation. Zbl 1359.92128
Hegland, Markus
1
2008
Markov process modelling of gene regulation. Zbl 1087.92020
Booth, Hilary S.; Burden, Conrad J.; Hegland, Markus; Santoso, Lucia
1
2005
A stochastic model of gene switches. Zbl 1074.92014
Santoso, Lucia; Booth, Hilary S.; Burden, Conrad J.; Hegland, Markus
1
2005
Additive models in high dimensions. Zbl 1078.65521
Hegland, Markus; Pestov, Vladimir
1
2005
Data mining techniques. Zbl 1123.68343
Hegland, Markus
1
2001
Scalable parallel algorithms for surface fitting and data mining. Zbl 0971.68214
Christen, Peter; Hegland, Markus; Nielsen, Ole M.; Roberts, Stephen; Strazdins, Peter E.; Atlas, Irfan
1
2001
Cluster analysis using triangulation. Zbl 0980.65012
Eldershaw, C.; Hegland, M.
1
1998
Can MARS be improved with B-splines? Zbl 0980.65503
Bakin, S.; Hegland, M.; Osborne, M.
1
1998
Parallel stable solution methods for tridiagonal linear systems of equations. Zbl 0909.65017
Dun, C. R.; Hegland, M.; Osborne, M. R.
1
1996
An implementation of multiple and multivariate Fourier transforms on vector processors. Zbl 0818.65148
Hegland, Markus
1
1995
A self-sorting in-place fast Fourier transform algorithm suitable for vector and parallel processing. Zbl 0808.65145
Hegland, Markus
1
1994
On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization. Zbl 0738.65015
Hegland, Markus
1
1991
Algorithm for the reconstruction of special Jacobi matrices from their eigenvalues. Zbl 0674.65015
Hegland, M.; Marti, J. T.
1
1989
Old wine in fractal bottles. I: Orthogonal expansions on self-referential spaces via fractal transformations. Zbl 1372.28006
Bandt, Christoph; Barnsley, Michael; Hegland, Markus; Vince, Andrew
4
2016
Spatially-dimension-adaptive sparse grids for online learning. Zbl 1356.68168
Khakhutskyy, Valeriy; Hegland, Markus
1
2016
Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces. Zbl 1311.65054
Hegland, Markus; Jin, Qinian; Wang, Wei
6
2015
Convergence rates in \(\ell^{1}\)-regularization when the basis is not smooth enough. Zbl 1325.65076
Flemming, Jens; Hegland, Markus
5
2015
Sparse grid quadrature on products of spheres. Zbl 1330.65045
Hegland, Markus; Leopardi, Paul
1
2015
Fault tolerant computation with the sparse grid combination technique. Zbl 1320.65206
Harding, Brendan; Hegland, Markus; Larson, Jay; Southern, James
1
2015
Numerics and fractals. Zbl 1305.28015
Barnsley, Michael F.; Hegland, Markus; Massopust, Peter
5
2014
Robust solutions to PDEs with multiple grids. Zbl 1316.65109
Harding, Brendan; Hegland, Markus
1
2014
On tractability of approximation in special function spaces. Zbl 1255.65042
Hegland, M.; Wasilkowski, G. W.
6
2013
A stabilised mixed finite element method for thin plate splines based on biorthogonal systems. Zbl 1390.65149
Lamichhane, Bishnu Prasad; Hegland, Markus
2
2012
A robust combination technique. Zbl 1390.65158
Harding, Brendan; Hegland, Markus
1
2012
Errors of regularisation under range inclusions using variable Hilbert scales. Zbl 1252.47009
Hegland, Markus; Hofmann, Bernd
2
2011
A finite element method for density estimation with Gaussian process priors. Zbl 1211.65007
Griebel, Michael; Hegland, Markus
6
2010
Parallelising the finite state projection method. Zbl 1386.65046
Sunkara, Vikram; Hegland, Markus
3
2010
On the numerical solution of the chemical master equation with sums of rank one tensors. Zbl 1386.65050
Hegland, Markus; Garcke, Jochen
2
2010
Derivative spectroscopy – an enhanced role for numerical differentiation. Zbl 1205.65130
Anderssen, R. S.; Hegland, M.
2
2010
Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities. Zbl 1204.65164
Hegland, Markus
1
2010
Fitting multidimensional data using gradient penalties and the sparse grid combination technique. Zbl 1166.65004
Garcke, Jochen; Hegland, Markus
10
2009
Sparse grids and hybrid methods for the chemical master equation. Zbl 1155.65304
Hegland, Markus; Hellander, Andreas; Lötstedt, Per
3
2008
The total quasi-steady state assumption: its justification by singular perturbation theory and its application to the chemical master equation. Zbl 1359.92129
Khoo, Chin Foon; Hegland, Markus
2
2008
Approximating the solution of the chemical master equation by aggregation. Zbl 1359.92128
Hegland, Markus
1
2008
A solver for the stochastic master equation applied to gene regulatory networks. Zbl 1121.65009
Hegland, Markus; Burden, Conrad; Santoso, Lucia; MacNamara, Shev; Booth, Hilary
22
2007
The combination technique and some generalisations. Zbl 1109.65052
Hegland, Markus; Garcke, Jochen; Challis, Vivien
22
2007
Approximate maximum a posteriori with Gaussian process priors. Zbl 1127.65039
Hegland, Markus
2
2007
Parallelisation of sparse grids for large scale data analysis. Zbl 1104.65009
Garcke, Jochen; Hegland, Markus; Nielsen, Ole
2
2006
Resolution enhancement of spectra using differentiation. Zbl 1080.65124
Hegland, Markus; Anderssen, Robert S.
4
2005
Markov process modelling of gene regulation. Zbl 1087.92020
Booth, Hilary S.; Burden, Conrad J.; Hegland, Markus; Santoso, Lucia
1
2005
A stochastic model of gene switches. Zbl 1074.92014
Santoso, Lucia; Booth, Hilary S.; Burden, Conrad J.; Hegland, Markus
1
2005
Additive models in high dimensions. Zbl 1078.65521
Hegland, Markus; Pestov, Vladimir
1
2005
Multidimensional smoothing using hyperbolic interpolatory wavelets. Zbl 1065.65007
Hegland, Markus; Nielsen, Ole M.; Shen, Zuowei
2
2004
Adaptive sparse grids. Zbl 1078.65520
Hegland, M.
18
2003
Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. Zbl 1041.65019
Roberts, Stephen; Hegland, Markus; Altas, Irfan
4
2003
Additive sparse grid fitting. Zbl 1036.65012
Hegland, Markus
2
2003
Parallel interior point schemes for solving multistage convex programming. Zbl 0993.90093
Hegland, M.; Osborne, M. R.; Sun, J.
2
2001
Data mining techniques. Zbl 1123.68343
Hegland, Markus
1
2001
Scalable parallel algorithms for surface fitting and data mining. Zbl 0971.68214
Christen, Peter; Hegland, Markus; Nielsen, Ole M.; Roberts, Stephen; Strazdins, Peter E.; Atlas, Irfan
1
2001
Finite element thin plate splines in density estimation. Zbl 0977.65003
Hegland, Markus; Hooker, Giles; Roberts, Stephen
3
2000
Parallel performance of fast wavelet transforms. Zbl 0973.65135
Nielsen, Ole Møller; Hegland, Markus
2
2000
For numerical differentiation, dimensionality can be a blessing! Zbl 0921.65018
Anderssen, Robert S.; Hegland, Markus
17
1999
A parallel solver for generalised additive models. Zbl 0942.62078
Hegland, M.; McIntosh, I.; Turlach, B. A.
3
1999
A stable finite difference ansatz for higher order differentiation of non-exact data. Zbl 0918.65017
Anderssen, Bob; de Hoog, Frank; Hegland, Markus
8
1998
A mollification framework for improperly posed problems. Zbl 0896.65042
Hegland, M.; Anderssen, R. S.
4
1998
Finite element thin plate splines for surface fitting. Zbl 1016.74066
Hegland, M.; Roberts, S.; Altas, I.
3
1998
On the stable parallel solution of general narrow banded linear systems. Zbl 0930.65017
Arbenz, Peter; Hegland, Markus
3
1998
Wrap-around partitioning for block bidiagonal linear systems. Zbl 0907.65035
Hegland, Markus; Osborne, Michael R.
3
1998
Cluster analysis using triangulation. Zbl 0980.65012
Eldershaw, C.; Hegland, M.
1
1998
Can MARS be improved with B-splines? Zbl 0980.65503
Bakin, S.; Hegland, M.; Osborne, M.
1
1998
The trade-off between regularity and stability in Tikhonov regularization. Zbl 0854.65123
Nair, M. Thamban; Hegland, Markus; Anderssen, Robert S.
7
1997
Real and complex fast Fourier transforms on the Fujitsu VPP 500. Zbl 0875.68489
Hegland, Markus
2
1996
Parallel stable solution methods for tridiagonal linear systems of equations. Zbl 0909.65017
Dun, C. R.; Hegland, M.; Osborne, M. R.
1
1996
Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization. Zbl 0841.65039
Hegland, Markus
22
1995
An implementation of multiple and multivariate Fourier transforms on vector processors. Zbl 0818.65148
Hegland, Markus
1
1995
A self-sorting in-place fast Fourier transform algorithm suitable for vector and parallel processing. Zbl 0808.65145
Hegland, Markus
1
1994
An optimal order regularization method which does not use additional smoothness assumptions. Zbl 0760.65053
Hegland, Markus
12
1992
On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization. Zbl 0738.65015
Hegland, Markus
1
1991
Algorithm for the reconstruction of special Jacobi matrices from their eigenvalues. Zbl 0674.65015
Hegland, M.; Marti, J. T.
1
1989
Numerical computation of least constants for the Sobolev inequality. Zbl 0626.46025
Hegland, M.; Marti, J. T.
3
1986
all top 5

Cited by 351 Authors

16 Hegland, Markus
8 Hofmann, Bernd
8 Pereverzev, Sergei V.
7 Nair, M. Thamban
6 Anderssen, Robert Scott
6 Griebel, Michael
6 Tautenhahn, Ulrich
5 Lötstedt, Per
5 Lu, Shuai
5 Tempone, Raúl F.
4 Bungartz, Hans-Joachim
4 Fu, Chuli
4 Gu, Ruixue
4 Haji-Ali, Abdul-Lateef
4 Han, Bo
4 Mathé, Peter
4 Nobile, Fabio
4 Pflüger, Dirk
4 Schieck, M.
4 Tamellini, Lorenzo
3 Benítez Lopez, Julio
3 Dolgov, Sergey V.
3 Hellander, Andreas
3 Jahnke, Tobias
3 Khoromskij, Boris N.
3 Nashed, M. Zuhair
3 Qian, Zhi
3 Shao, Yuanyuan
3 Xu, Guiqiao
2 Beck, Joakim
2 Bersani, Alberto Maria
2 Borri, Alessandro
2 Böttcher, Albrecht
2 Burrage, Kevin
2 Cao, Yang
2 de Hoog, Frank Robert
2 Dinh Dũng
2 Engblom, Stefan
2 Farcas, Ionut-Gabriel
2 Feng, Xiaoli
2 Ferm, Lars
2 Freeden, Willi
2 Garcke, Jochen
2 Gerth, Daniel
2 Gnewuch, Michael
2 Harbrecht, Helmut
2 Harding, Brendan
2 Hefter, Mario
2 Hinrichs, Aicke
2 Hohage, Thorsten
2 Hullmann, Alexander
2 Jakeman, John Davis
2 Lamichhane, Bishnu Prasad
2 MacNamara, Shev F.
2 Madden, Niall
2 Massopust, Peter R.
2 Neckel, Tobias
2 Peherstorfer, Benjamin
2 Rakočević, Vladimir
2 Ritter, Klaus
2 Roberts, Stephen Gwyn
2 Russell, Stephen J.
2 Stals, Linda
2 Tong, Shanshan
2 Vince, Andrew
2 Viswanathan, Puthan Veedu
2 Wang, Wei
2 Wang, Yanbo
2 Wasilkowski, Grzegorz W.
2 Watson, Layne Terry
2 Wei, Ting
2 Yamamoto, Masahiro
2 Zhang, Jingwei
2 Zhao, Zhenyu
1 Abel, Markus
1 Acebrón, Juan A.
1 Ahnert, Karsten
1 Alemazkoor, Negin
1 Altıntan, Derya
1 Amodio, Pierluigi
1 Archibald, Richard
1 Baer, Ashley
1 Barnsley, Michael Fielding
1 Beattie, Christopher A.
1 Beliakov, Gleb
1 Bersani, Enrico
1 Bohn, Bastian
1 Booth, Hilary S.
1 Boyd, Stephen Poythress
1 Brown-Dymkoski, Eric
1 Buescu, Jorge
1 Burden, Conrad John
1 Burrage, Pamela M.
1 Butler, Tom
1 Buttari, Alfredo
1 Caboussat, Alexandre
1 Cameron, David C.
1 Capodaglio, Giacomo
1 Carravetta, Francesco
1 Cash, Jeff R.
...and 251 more Authors
all top 5

Cited in 84 Serials

11 Journal of Complexity
9 Journal of Computational Physics
9 SIAM Journal on Scientific Computing
9 Journal of Inverse and Ill-Posed Problems
7 Mathematics of Computation
7 Applied Mathematics and Computation
7 Journal of Computational and Applied Mathematics
5 Numerische Mathematik
5 Journal of Scientific Computing
4 Computers & Mathematics with Applications
4 Computer Methods in Applied Mechanics and Engineering
4 Applied Numerical Mathematics
4 Numerical Linear Algebra with Applications
4 Inverse Problems in Science and Engineering
3 Inverse Problems
3 BIT
3 Numerical Functional Analysis and Optimization
3 Journal of Integral Equations and Applications
3 Numerical Algorithms
2 Applicable Analysis
2 Bulletin of the Australian Mathematical Society
2 Journal of Mathematical Analysis and Applications
2 Journal of Mathematical Biology
2 Chaos, Solitons and Fractals
2 Automatica
2 Computing
2 Integral Equations and Operator Theory
2 SIAM Journal on Numerical Analysis
2 Linear Algebra and its Applications
2 Computational Statistics and Data Analysis
2 Advances in Computational Mathematics
2 Mathematical Problems in Engineering
2 Foundations of Computational Mathematics
2 Computational Methods in Applied Mathematics
2 Analysis and Applications (Singapore)
2 GEM - International Journal on Geomathematics
2 Journal of Theoretical Biology
1 The Canadian Journal of Statistics
1 Computers and Fluids
1 Computer Physics Communications
1 Linear and Multilinear Algebra
1 Mathematical Notes
1 Ukrainian Mathematical Journal
1 Bulletin of Mathematical Biology
1 Acta Mathematica Vietnamica
1 Calcolo
1 Journal of Approximation Theory
1 Journal of Differential Equations
1 Journal of Optimization Theory and Applications
1 Monatshefte für Mathematik
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Zeitschrift für Analysis und ihre Anwendungen
1 Constructive Approximation
1 Applied Mathematics Letters
1 SIAM Journal on Matrix Analysis and Applications
1 Annals of Operations Research
1 International Journal of High Speed Computing
1 Computational Statistics
1 Applied Mathematical Modelling
1 European Journal of Operational Research
1 SIAM Journal on Applied Mathematics
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Continuum Mechanics and Thermodynamics
1 Applied and Computational Harmonic Analysis
1 The Journal of Fourier Analysis and Applications
1 Parallel Algorithms and Applications
1 Doklady Mathematics
1 Journal of the Royal Statistical Society. Series B. Statistical Methodology
1 Engineering Computations
1 Optimization and Engineering
1 The ANZIAM Journal
1 International Journal of Computational Methods
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 Frontiers of Mathematics in China
1 Inverse Problems and Imaging
1 EURASIP Journal on Advances in Signal Processing
1 Journal of Statistical Theory and Practice
1 Algorithms
1 Science China. Mathematics
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
1 Bayesian Analysis
1 Journal of Fractal Geometry
1 Special Matrices
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys

Citations by Year