By Dr Quoc Thong Le Gia

Books

Pesenson I; Gia QTL; Mayeli A; Mhaskar H; Zhou D-X, 2017, Frames and Other Bases in Abstract and Function Spaces Novel Methods in Harmonic Analysis, Birkhäuser

Pesenson I; Gia QTL; Mayeli A; Mhaskar H; Zhou D-X, 2017, Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science Novel Methods in Harmonic Analysis, Birkhäuser

Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou DX, 2017, Preface

Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou DX, 2017, Preface

, 2017, Frames and Other Bases in Abstract and Function Spaces, Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou D-X, (eds.), Springer International Publishing, http://dx.doi.org/10.1007/978-3-319-55550-8

, 2017, Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou D-X, (eds.), Springer International Publishing, http://dx.doi.org/10.1007/978-3-319-55556-0

Hubbert S; Le Gia QT; Morton TM, 2015, Spherical Radial Basis Functions, Theory and Applications, Springer

Hubbert S; Gia QTL; Morton TM, 2015, Preface, http://dx.doi.org/10.1525/9780520947436-001

Book Chapters

Hubbert S; Lê Gia QT; Morton TM, 2015, 'Error Bounds via Duchon’s Technique', in SpringerBriefs in Mathematics, pp. 59 - 83, http://dx.doi.org/10.1007/978-3-319-17939-1_3

Hubbert S; Lê Gia QT; Morton TM, 2015, 'Fast Iterative Solvers for PDEs on Spheres', in SpringerBriefs in Mathematics, pp. 97 - 119, http://dx.doi.org/10.1007/978-3-319-17939-1_5

Hubbert S; Lê Gia QT; Morton TM, 2015, 'Motivation and Background Functional Analysis', in SpringerBriefs in Mathematics, pp. 1 - 28, http://dx.doi.org/10.1007/978-3-319-17939-1_1

Hubbert S; Lê Gia QT; Morton TM, 2015, 'Parabolic PDEs on Spheres', in SpringerBriefs in Mathematics, pp. 121 - 138, http://dx.doi.org/10.1007/978-3-319-17939-1_6

Hubbert S; Lê Gia QT; Morton TM, 2015, 'Radial Basis Functions for the Sphere', in SpringerBriefs in Mathematics, pp. 85 - 95, http://dx.doi.org/10.1007/978-3-319-17939-1_4

Hubbert S; Lê Gia QT; Morton TM, 2015, 'The Spherical Basis Function Method', in SpringerBriefs in Mathematics, pp. 29 - 58, http://dx.doi.org/10.1007/978-3-319-17939-1_2

Journal articles

Hamann J; Le Gia QT; Sloan IH; Womersley RS, 2024, 'Removing the Mask—Reconstructing a Real-Valued Field on the Sphere from a Masked Field by Spherical Fourier Analysis', SIAM Journal on Imaging Sciences, 17, pp. 1820 - 1843, http://dx.doi.org/10.1137/23m1603157

Alodat T; Le Gia QT; Sloan IH, 2024, 'On approximation for time-fractional stochastic diffusion equations on the unit sphere', Journal of Computational and Applied Mathematics, 446, http://dx.doi.org/10.1016/j.cam.2024.115863

Le Gia QT; Mhaskar H, 2023, 'Numerical solutions to an inverse problem for a non-linear Helmholtz equation', ANZIAM Journal, 64, http://dx.doi.org/10.21914/anziamj.v64.17954

Zhong M; Gia QTL; Sloan IH, 2023, 'A Multiscale RBF Method for Severely Ill-Posed Problems on Spheres', Journal of Scientific Computing, 94, http://dx.doi.org/10.1007/s10915-022-02046-9

Buratti Y; Dick J; Le Gia Q; Hameiri Z, 2022, 'Deep learning extraction of the temperature-dependent parameters of bulk defects', ACS Applied Materials and Interfaces, 14, pp. 48647 - 48657, http://dx.doi.org/10.1021/acsami.2c12162

Hesse K; Le Gia QT, 2022, 'L2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data', Journal of Computational and Applied Mathematics, 408, http://dx.doi.org/10.1016/j.cam.2022.114118

Le Gia QT; Clarke M; Dick J; Pye D, 2022, 'Elasticity equations with random domains—the shape derivative approach', ANZIAM Journal, 62, pp. c256 - c272, http://dx.doi.org/10.21914/anziamj.v62.16120

Le Gia QT; Li M; Wang YG, 2021, 'Algorithm 1018: FaVeST-Fast Vector Spherical Harmonic Transforms', ACM Transactions on Mathematical Software, 47, http://dx.doi.org/10.1145/3458470

Brzeźniak Z; Dhariwal G; Le Gia QT, 2021, 'Stochastic Navier–Stokes Equations on a Thin Spherical Domain', Applied Mathematics and Optimization, 84, pp. 1971 - 2035, http://dx.doi.org/10.1007/s00245-020-09702-2

Hamann J; Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2021, 'A new probe of Gaussianity and isotropy with application to cosmic microwave background maps', International Journal of Modern Physics C, 32, http://dx.doi.org/10.1142/S0129183121500844

Lamichhane BP; Harris E; Le Gia QT, 2021, 'Approximation of noisy data using multivariate splines and finite element methods', Journal of Algorithms and Computational Technology, 15, http://dx.doi.org/10.1177/17483026211008405

Buratti Y; Le Gia QT; Dick J; Zhu Y; Hameiri Z, 2020, 'Extracting bulk defect parameters in silicon wafers using machine learning models', npj Computational Materials, 6, http://dx.doi.org/10.1038/s41524-020-00410-7

Peach JJ; Le Gia QT, 2019, 'A spectral method to the stochastic Stokes equations on the sphere', ANZIAM Journal, 60, pp. C52 - C64, http://dx.doi.org/10.21914/anziamj.v60i0.13987

Kazashi Y; Le Gia QT, 2019, 'A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere', Journal of Complexity, 50, pp. 43 - 65, http://dx.doi.org/10.1016/j.jco.2018.09.001

Dick J; Gantner RN; Le Gia QT; Schwab C, 2019, 'Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion', Computers and Mathematics with Applications, 77, pp. 144 - 172, http://dx.doi.org/10.1016/j.camwa.2018.09.019

Gia QTL; Sloan IH; Womersley RS; Wang YG, 2019, 'Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere', Applied and Computational Harmonic Analysis, http://dx.doi.org/10.1016/j.acha.2019.01.005

Le Gia QT, 2018, 'Numerical solutions of a boundary value problem on the sphere using radial basis functions', , pp. 815 - 836, http://dx.doi.org/10.1007/978-3-319-72456-0_36

Zhong M; Le Gia QT; Wang W, 2018, 'A multiscale support vector regression method on spheres with data compression', Applicable Analysis, http://www.tandfonline.com/doi/full/10.1080/00036811.2018.1430783

Brzeźniak Z; Goldys B; Gia QTL; Le Gia Q, 2017, 'Random attractors for the stochastic Navier--Stokes equations on the 2D unit sphere', Journal of Mathematical Fluid Mechanics, 20, pp. 227 - 253, http://dx.doi.org/10.1007/s00021-017-0351-4

Wang YG; Le Gia QT; Sloan IH; Womersley RS, 2017, 'Fully discrete needlet approximation on the sphere', Applied and Computational Harmonic Analysis, 43, pp. 292 - 316, http://dx.doi.org/10.1016/j.acha.2016.01.003

Dinh Nguyen Duy H; Nguyen Huy T; Le Dinh L; Quoc Thong Le G, 2017, 'Inverse problem for nonlinear backward space-fractional diffusion equation', Journal of Inverse and Ill-Posed Problems, 25, pp. 423 - 443, http://dx.doi.org/10.1515/jiip-2015-0065

Le Gia QT; Sloan IH; Wendland H, 2017, 'Zooming from global to local: a multiscale RBF approach', Advances in Computational Mathematics, 43, pp. 581 - 606, http://dx.doi.org/10.1007/s10444-016-9498-4

Dick J; Gantner RN; Le Gia QT; Schwab C, 2017, 'Multilevel higher-order quasi-Monte Carlo Bayesian estimation', Mathematical Models and Methods in Applied Sciences, 27, pp. 953 - 995, http://dx.doi.org/10.1142/S021820251750021X

Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2017, 'Needlet approximation for isotropic random fields on the sphere', Journal of Approximation Theory, 216, pp. 86 - 116, http://dx.doi.org/10.1016/j.jat.2017.01.001

Zhu Y; Le Gia QT; Juhl MK; Coletti G; Hameiri Z, 2017, 'Application of the Newton–Raphson method to lifetime spectroscopy for extraction of defect parameters', IEEE Journal of Photovoltaics, 7, pp. 1092 - 1092, http://dx.doi.org/10.1109/JPHOTOV.2017.2695666

Chernih A; Le Gia QT, 2016, 'Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains', Advances in Computational Mathematics, 42, pp. 1187 - 1208, http://dx.doi.org/10.1007/s10444-016-9458-z

Le Gia QT; Tran, T ; Nguyen HT, 2016, 'Solving the backward heat equation on the unit sphere', ANZIAM Journal : Electronic Supplement, pp. C262 - C278, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/9346

Dick J; Le Gia QT; Schwab C, 2016, 'Higher order quasi-monte carlo integration for holomorphic, parametric operator equations', SIAM-ASA Journal on Uncertainty Quantification, 4, pp. 48 - 79, http://dx.doi.org/10.1137/140985913

Dick J; Kuo FY; Le Gia QT; Schwab C, 2016, 'Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations', SIAM Journal on Numerical Analysis, 54, pp. 2541 - 2568, http://dx.doi.org/10.1137/16M1078690

Brzeźniak Z; Goldys B; Le Gia QT, 2015, 'Random dynamical systems generated by stochastic Navier-Stokes equations on a rotating sphere', Journal of Mathematical Analysis and Applications, 426, pp. 505 - 545, http://dx.doi.org/10.1016/j.jmaa.2015.01.054

Dick J; Kuo FY; Gia QTL; Schwab C; Le Gia Q, 2015, 'Fast QMC matrix-vector multiplication', SIAM Journal on Scientific Computing, 37, pp. A1436 - A1450, http://dx.doi.org/10.1137/151005518

Le Gia QT; Wendland H, 2014, 'Data compression on the sphere using multiscale radial basis function approximation', Advances in Computational Mathematics, 40, pp. 923 - 943, http://dx.doi.org/10.1007/s10444-013-9334-z

Chernih A; Le Gia QT, 2014, 'Multiscale methods with compactly supported radial basis functions for Galerkin approximation of elliptic PDEs', IMA Journal of Numerical Analysis, 34, pp. 569 - 591, http://dx.doi.org/10.1093/imanum/drt004

Le Gia QT; McLean W, 2014, 'Solving the heat equation on the unit sphere via Laplace transforms and radial basis functions', Advances in Computational Mathematics, 40, pp. 353 - 375, http://dx.doi.org/10.1007/s10444-013-9311-6

Dick J; Kuo FY; Le Gia QT; Nuyens D; Schwab C, 2014, 'Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs', SIAM Journal on Numerical Analysis, 52, pp. 2676 - 2702, http://dx.doi.org/10.1137/130943984

Le Gia QT; Tran T, 2012, 'Fast iterative solvers for boundary value problems on a local spherical region', Proceedings of the 16th Computational Techniques and Applications Conference, published in ANZIAM Journal, 54, pp. C492 - C507, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6303/1730

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