2023 Lai, M. -J., Xie, Jiaxin and Xu, Zhiqiang, Graph Sparsification by Universal Greedy Algorithms, Journal of Computational Math, vol. ?? (2023) pp. Published online Shen, Z. M., Lai, M. -J. and Li, S.., Graph-based Semi-supervised Local Clustering with Few Labeled Nodes, accepted, IJCAI , (2023) Lai, M. -J. and Lee, J., Trivariate Spline based Collocation Methods for Numerical Solution to 3D Monge-Ampere Equations, Published On-lne , Journal of Scientific Computing, (2023) Feng, R. Z., Huang, A., Lai, M. -J. and Shen, Z. M., Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method, Journal of Computational Math, vol. 41 (2023) pp. 18--38. Lai, M. -J. and Shen, Z., A compressed sensing based least squares approach to semi-supervised local cluster extraction. J. Sci. Comput. 94 (2023), no. 3, Paper No. 63, 23 pp. 2022 Deng, Chongyang and Lai, M. -J., On e-Locality of Harmonic Generalized Barycentric Coordinatesi and Their Application to Solution of the Poisson Equation, to appear , Pure and Applied Functional Analysis , (2022) Deng, Chongyang, Hu, Tsung-Wei and Lai, M. -J., The Harmonic GBC Function Map is a Bijection if the Target Domain is Convex, submitted , (2022) Lai, M. -J. and Lee, J., A Multivariate Spline based Collocation Method for Numerical Solution of PDEs, SIAM J. Numerical Analysis, vol. 60 (2022) pp. 2405--2434 Lai, M. -J. and Shen, Z. M., The Kolmogorov Superposition theorem can break the curse of dimensionality when approximating high dimensional functions, submitted, (2022) Lai, M. -J., Xie, Jiaxin and Xu, Zhiqiang, Graph Sparsification by Universal Greedy Algorithms, Journal of Computational Math, vol. ?? (2022) pp. to appear Lai, M. -J. and Shen, Z., An effective approach to semi-supervised cluster extraction , to appear , Journal of Scientific Computing , (2022) Lai, M. -J. and Lanterman, J., Construction of C1 Polygonal Splines over Quadrilateral Partition, Computer Aided Geometric Design, vol. 92 (2022) pp. Paper No.102063 2021 Lai, M. -J. and Wang, Y., Sparse Solutions of Underdetermined Linear Systems and Their Applications, SIAM Publication, (2021) Lai, M. -J., Liu, Y., Li, S. and Wang, H., On the Schatten p norm minimization for low rank matrix recovery, Applied Comput. Harmonic Analysis, vol. 51 (2021) pp. 157--170. Huang, Meng, Lai, M. -J., Varghese, Abraham and Xu, Zhiqiang, On DC based methods for Phase Retrieval, Approximation Theory XVI: San Antonio, 2019, Springer Verlag , (2021) edited by G. Fasshauer, M. Neamtu, and L. L. Schumaker Deng, Chongyang, Hong, Q. F., Lai, M. -J., Mersmann, Clayton and Xu, Yidong, Multivariate Splines for Curve and Surface Interpolation and Fitting, submitted , (2021) Lai, M. -J. and Lee, J., A Multivariate Spline based Collocation Method for Numerical Solution of PDEs, submitted , (2021) 2020 Lai, M. -J. and Mckenzie, Daniel., Compressive Sensing Approach to Cut Improvement and Local Clustering , SIAM J. Math. Data Science, vol. 2 (2020) pp. 368--395. Deng, Chongyang, Fan, X. Li. and Lai, M. -J., A minimization approach for constructing generalized barycentric coordinates and its computation, J. of Scientific Computing, vol. 84 (2020) Wang, L., Wang, G., Lai, M. -J. and Gao, L., Efficient Estimation of Partially Linear Models for Spatial Data over Complex Domains, Statistica Sinica, vol. 30 (2020) pp. 347--360 Gao, Fuchang and Lai, M. -J., A new H2 regularity condition of the solution to Dirichlet problem of the Poisson equation and its applications, Acta Mathematica Sinica, vol. 36 (2020) pp. 21--39 2019 Hong, Qianying, Lai, M. -J., Messi, Leopold Matamba and Wang, Jingyue, Galerkin method with splines for total variation minimization, J. Algorithms Computational Technology , vol. 13 (2019) pp. 1--16 Kang, Hongmei, Lai, M. -J. and Li, Xin, An economecal representation of PDE solution by using compressive sensing approach, J. Computer Aided Design , vol. 115 (2019) pp. 78--86 Kapita, S. and Lai, M. -J., A bivariate spline Soluton to the Exterior Helmholtz Equation and Its Applications, submitted , (2019) Lai, M. -J. and Mersmann, C., A bivariate spline Soluton of Helmholtz Equation with large wave number, submitted , (2019) Wen, Jinming, Zhou, Zhengchun, Liu, Zilong, Lai, M. -J. and Tang, Xiaohu, Sharp sufficient conditions for stable recovery of block sparse signals b y block orthogonal matching pursuit, Applied and Computational Harmonic Analysis, (2019) pp. 948--974 2018 Baramidze, V. and Lai, M. -J., Nonnegative Data Interpolation by Spherical Splines, J. Applied and Comput. Math., vol. 342 (2018) pp. 463--477 Lai, M. -J. and Wang, C. M., A bivariate spline method for 2nd order elliptic equations in non-diverge nce form, Journal of Scientific Computing , (2018) pp. 803--829 2017 Lai, M. -J. and Varghese, Abraham, On Convergence of the Alternating Projection Method for Matrix Completion and Sparse Recovery Problems , submitted , (2017) Lai, M. -J. and Mersmann, C., Adaptive Triangulation Methods for Bivariate Spline Solutions of PDEs, Approximation Theory XV: San Antonio, 2016, Springer Verlag, (2017) edited by G. Fasshauer and L. L. Schumaker pp. 155--175. Lai, M. -J. and Lanterman, J., A polygonal spline method for general 2nd order elliptic equations and its applications, Approximation Theory XV: San Antonio, 2016, Springer Verlag, (2017) edited by G. Fasshauer and L. L. Schumaker pp. 119--154. Lai, M. -J., Max-Norm Estimate of Spline Solution to Second Order Elliptic PDE in Nondivergence Form, submitted, (2017) Deng, W., Lai, M. -J., Peng, Z. and Yin, W. T., Parallel Multi-Block ADMM with o(1/k) Convergence, Journal of Scientific Computing>, vol. 71 (2017) pp. 712--736. 2016 Lai, M. -J. and Slavov, G., On Recursive Refinement of Convex Polygons, Computer Aided Geometric Design, vol. 45 (2016) pp. 83--90. Floater, M. and Lai, M. -J., Polygonal spline spaces and the numerical solution of the Poisson equation, SIAM Journal on Numerical Analysis, (2016) pp. 797--824. Download Code Liu, X. , Guillas, S. and Lai, M. -J., Efficient spatial modeling using the SPDE approach with bivariate splines, Journal of Computational and Graphical Statistics , vol. 25 (2016) pp. 1176--1194. 2015 Gutierrez, J. , Lai, M. -J. and Slavov, G., Bivariate Spline Solution of Time Dependent Nonlinear PDE for a Population Density over Irregular Domains, Mathematical Biosciences, vol. 270 (2015) pp. 263--277. An expanded and corrected version can be found below. Gutierrez, J. , Lai, M. -J. and Slavov, G., Bivariate Spline Solution of Time Dependent Nonlinear PDE for a Population Density over Irregular Domains, Mathematical Biosciences, vol. 270 (2015) pp. 263--277. Lai, M. -J. and Meile, C., Scattered data interpolation with nonnegative preservation using bivariate splines, Computer Aided Geometric Design, vol. 34 (2015) pp. 37--49. Wang, Z., Lai, M. -J., Lu, Z., Fan, W., Davulcu, H. and Ye, J., Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion, A488--A514, SIAM Journal of Scientific Computing, vol. 37 (2015) Lai, M. -J. and Liu, L. Y., The Probabilitic Estimates on the Largest and Smallest $q$-singular Values of Random Matrices, Mathematics of Computation, vol. 84 (2015) pp. 1775--1794. 2014 Hong, Q. Y., Lai, M. -J. and Messi, L. M., The Rayleigh-Ritz Method for Total Variation Minimization Using Bivariate Splines Functions on Triangulation, submitted, (2014) Meile, C., Lai, M. -J., Bracco, A.., Luo, H. and Joye, S., Interpretation of oxygen profiles in the aftermath of the BP/Deepwater Horizon hydrocarbon discharge , submitted, (2014) Lai, M. -J. and Messi, L. M., Multiscale Hierarchical Decompositon: Modes and Rates of Convergence, submitted, (2014) Lin, B., Li, Q., Sun, Q., Lai, M. -J., Davison, I.., Fan, W. and Ye, J., Stochastic Coordinate Coding and Its Application for Drosophila Gene Expression Pattern Annotation, submitted, (2014) Wang, Z., Lai, M. -J., Lu, Z. and Ye, J., Orthogonal Rank One Matrix Pursuit for Matrix Completion, appeared, International Conference on Machine Learning (ICML) , (2014) 2013 Lai, M. -J. and Matt, M., A Cr Trivariate Macro-Element Based on Alfeld Split, Journal of Approximation Theory, vol. 175 (2013) pp. 114--131. Guo, W. H. and Lai, M. -J., Box Spline Wavelet Frames for Image Edge Analysis, SIAM Journal Imaging Sciences, vol. 6 (2013) pp. 1553--1578. Lai, M. -J. and Yin, W. T., Augmented L1 and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm, SIAM Journal Imaging Sciences, vol. 6 (2013) pp. 1059--1091. Lai, M. -J. and Meile, C., Wator Column Oxygen Anomalies in the Aftermath of the BP Oil Spill, a poster in a Gulf of Mexico Research Initiative conference, (2013) Lai, M. -J. and Zhou, T., Scattered data interpolation by bivariate splines with higher approximation order, Journal of Computational and Applied Mathematics, vol. 242 (2013) pp. 125--140 Lai, M. -J. and Wang, L., Bivariate penalized splines for regression, Statistica Sinica, vol. 23 (2013) pp. 1399--1417 Lai, M. -J. and Messi, L. M., Piecewise Linear Approximation of the continuous Rudin-Osher-Fatemi model for image denoising, SIAM Journal on Numerical Analysis, vol. 50 (2013) pp. 2446--2466 Lai, M. -J., Xu, Y. Y. and Yin, W. T., Improved Iteratively Reweighted Least Squares for Unconstrained Smoothed lp Minimization , SIAM Journal on Numerical Analysis, vol. 51 (2013) pp. 927--957 2012 Lai, M. -J., Li, S., Liu, L. Y. and Wang, H., Two Results on the Schatten p-quasi-norm minimization for low rank matrix recovery , submitted, (2012) Hong, Q., Lai, M. -J. and Wang, J., Convergence Analysis of a Finite Difference Scheme for the Gradient Flow associated with the ROF Model, submitted, (2012) Lai, M. -J. and Meile, C., Oxygen Anomalies in the Aftermath of the BP oil spill, a poster in a conference, (2012) Ettinger, B., Guillas, S. and Lai, M. -J., Bivariate Splines for Functional Regression Models with Application to Ozone Forecasting, Environmetrics, vol. 23 (2012) pp. 317--328 2011 Lai, M. -J., Pan, R. and Zhao, K., Initial Boundary Value Problem for 2D Viscous Boussinesq Equation, Arch Rational Mech Anal, vol. 199 (2011) pp. 739--760 Lai, M. -J. and Wang, J., An Unconstrained l_q Minimization for Sparse Solution of Underdetermined Linear Systems, SIAM Journal of Optimization, vol. 21 (2011) pp. 82--101 Lai, M. -J. and Liu, L. Y., The Null Space Property for Sparse Recovery From Multiple Measurement Vectors, Applied and Computational Harmonic Analysis, vol. 30 (2011) pp. 402--406 Baramidze, V. and Lai, M. -J., Convergence of Discrete and Penalized Least Squares of Spherical Splines, Journal of Approximation Theory, (2011) pp. 1091--1106 Hong, Q. and Lai, M. -J., A Bivariate Spline Approach for Image Enhancement, manuscript, (2011) 2010 Lai, M. -J. and Petukhov, A., Method of Virtual Components in the Multivariate Setting, Journal of Fourier Analysis and Its Applications, vol. 16 (2010) pp. 471--494 Foucart, S. and Lai, M. -J., Sparse Recovery with Pre-Gaussian Random Matrices, Studia Mathematica, vol. 200 (2010) pp. 91--102 Lai, M. -J., On Sparse Solution of Underdetermined Linear Systems, Journal of Concrete and Applicable Mathematics, vol. 8 (2010) pp. 296--327 Guillas, S. and Lai, M. -J., Bivariate Splines for Spatial Functional Regression Models, Journal of Nonparametric Statistics, vol. 22 (2010) pp. 477--497 2009 Lai, M. -J. and Schumaker, L. L., Domain Decomposition Method for Scattered Data Fitting, SIAM Journal on Numerical Analysis, vol. 47 (2009) pp. 911-928 Foucart, S. and Lai, M. -J., Sparsest Solutions of Underdetermined Linear Systems via $\ell_q$-minimization for $0\le q \le 1$, Applied and Computational Harmonic Analysis, vol. 26 (2009) pp. 395--407 Lai, M. -J., Shum, C. K., Baramidze, V. and Wenston, P., Triangulated Spherical Splines for Geopotential Reconstruction, Journal of Geodesy, vol. 83 (2009) pp. 695--708 Lai, M. -J., Lucier, B. and Wang, J., The Convergence of a Central Difference Discretization of Rudin-Osher-Fatemi Model for Image Denoising, Proceedings of SSVM, (2009) edited by X. C. Tai et al pp. 514--526 2008 Zhou, T., Han, D. and Lai, M. -J., Energy Minimization Method for Scattered Data Hermite Interpolation, Journal of Applied Numerical Mathematics, vol. 58 (2008) pp. 646--659 Kersey, S. and Lai, M. -J., Convergence of Local Variational Spline Interpolation, Journal of Mathematical Analysis and Applications, vol. 314 (2008) pp. 398--415 Lai, M. -J. and Nam, K., On the Number of Tight Wavelet Framelets Associated with Multivariate Box Splines, Journal of Approximation Theory and its Application, (2008) Lai, M. -J., Multivariate splines for Data Fitting and Approximation, the conference proceedings of the 12th Approximation Theory, San Antonio, Nashboro Press, (2008) edited by M. Neamtu and Schumaker, L. L. pp. 210--228 2007 Lai, M. -J. and Schumaker, L. L., Spline Functions over Triangulations, Cambridge University Press, (2007) Lai, M. -J. and Schumaker, L. L., Trivariate $C^r$ Polynomial Macro-elements, Constructive Approximation, vol. 26 (2007) pp. 11--28 Lai, M. -J. and Petukhov, A., The Method of Virtual Components for Constructing Wavelet Frames, Applied and Computational Harmonic Analysis, vol. 22 (2007) pp. 304--318 Lai, M. -J., Convergence of three $L_1$ Spline Methods for Data Interpolation and Fitting, Journal of Approximation Theory, vol. 145 (2007) pp. 196--211 Hu, X., Han, D. and Lai, M. -J., Bivariate Splines of Various Degrees for Numerical Solution of PDE, SIAM Journal of Scientific Computing, vol. 29 (2007) pp. 1338--1354 2006 Chen, G. R. and Lai, M. -J., Wavelets and Splines, Athens, 2005, Nashboro Press, (2006) Lai, M. -J., Construction of Multivariate Compactly Supported Orthonormal Wavelets, Advances in Computational Mathematics, vol. 25 (2006) pp. 41--56 Baramidze, V., Lai, M. -J. and Shum, C. K., Spherical Splines for Data Interpolation and Fitting, SIAM Journal of Scientific Computing, vol. 28 (2006) pp. 241--259 Geronimo, J. and Lai, M. -J., Factorization of Multivariate Positive Laurent Polynomials, Journal of Approximation Theory, vol. 139 (2006) pp. 327--345 Lai, M. -J. and Stoeckler, J., Construction of Multivariate Compactly Supported Tight Wavelet Frames, Applied and Computational Harmonic Analysis, vol. 21 (2006) pp. 324--348 Lai, M. -J., Construction of Multivariate Compactly Supported Prewavelets in $L_2$ spaces and pre-Riesz Basis in Sobolev Spaces, Journal of Approximation Theory, vol. 142 (2006) pp. 83--115 Lai, M. -J., Le Mehaute, A. and Sorokina, T., An Octahedral C^2 Macro-Element, Computer Aided Geometric Design, vol. 23 (2006) pp. 640--654 Awanou, G., Lai, M. -J. and Wenston, P., The Multivariate Spline Method for Scattered Data Fitting and Numerical Solution of Partial Differential Equations, Wavelets and Splines, Nashboro Press, (2006) edited by G. Chen and Lai, M. -J. pp. 24--74 Baramidze, V. and Lai, M. -J., Spherical Spline Solution to a PDE on the Sphere, Wavelets and Splines, Nashboro Press, (2006) edited by G. Chen and Lai, M. -J. pp. 75--92 Cho, O. and Lai, M. -J., A Class of Compactly Supported Orthonormal B-Spline wavelets, Wavelets and Splines, Nashboro Press, (2006) edited by G. Chen and Lai, M. -J. pp. 123--151 Lai, M. -J., Lian, J. A. and Cassidy, P., Removal of Gaps among Compound C^1 Bi-Cubic Parametric B-spline Surfaces, Wavelets and Splines, Nashboro Press, (2006) edited by G. Chen and Lai, M. -J. pp. 287--313 Lai, M. -J. and Nam, K., Tight Wavelet Frames over Bounded Domains, Wavelets and Splines, Nashboro Press, (2006) edited by G. Chen and Lai, M. -J. pp. 314--327 2005 Awanou, G. and Lai, M. -J., Trivariate Spline Approximations of 3D Navier-Stokes Equations, Mathematics of Computation, vol. 74 (2005) pp. 585--601 Awanou, G. and Lai, M. -J., On Convergence Rate of the Augmented Lagrangian Algorithm for Nonsymmetric Saddle Point Problems, Journal of Applied Numerical Mathematics, vol. 54 (2005) pp. 122--134 Wang, X. H., Wang, H. and Lai, M. -J., Some Results on Numerical Divided Difference Formulas, Scientia Sinica, vol. Ser. A., 35 (2005) pp. 712--720 Baramidze, V. and Lai, M. -J., Error Bounds for Minimal Energy Interpolatory Spherical Splines, Approximation Theory XI, Nashboro Press, (2005) pp. 25--50 2004 Lai, M. -J. and Wenston, P., $L^1$ Spline Methods for Scattered Data Interpolation and Approximation, Advances in Computational Mathematics, vol. 21 (2004) pp. 293--315 Lai, M. -J. and Le Mehaute, A., A New Kind of Trivariate C^1 Spline Space, Advances in Computational Mathematics, vol. 21 (2004) pp. 273--292 Lai, M. -J., Liu, C. and Wenston, P., On Two Nonlinear Biharmonic Evolution Equations: Existence, Uniqueness and Stability, Applicable Analysis, vol. 83 (2004) pp. 541--562 Lai, M. -J., Liu, C. and Wenston, P., Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations, Applicable Analysis, vol. 83 (2004) pp. 563--577 Lai, M. -J. and Wenston, P., Bivariate Splines for Fluid Flows, Computers and Fluids, vol. 33 (2004) pp. 1047--1073 Wang, X. H., Lai, M. -J. and Yang, S., On Divided Differences of the Remainder of Polynomial Interpolation, Journal of Approximation Theory, vol. 127 (2004) pp. 193--197 Baramidze, V. and Lai, M. -J., Volume Data Interpolation by Tensor Products of Spherical and Radial Splines, Advances in Constructive Approximation, Nashboro Press, (2004) edited by M. Neamtu and E. Saff pp. 75--88 2003 Lai, M. -J. and Schumaker, L. L., Macro-Elements and Stable Local Bases for Splines on Powell-Sabin Triangulations, Mathematics of Computation, vol. 72 (2003) pp. 335--354 Lai, M. -J., Liu, C. and Wenston, P., Bivariate Spline Method for Numerical Solution of Time Evolution Navier-Stokes Equations over Polygons in Stream Function Formulation, Numerical Methods for P.D.E., vol. 19 (2003) pp. 776--827 He, W. and Lai, M. -J., Construction of Trivariate Compactly Supported Biorthogonal Box Spline Wavelets, Journal of Approximation Theory, vol. 120 (2003) pp. 1--19 2002 Wang, X. H., Li, C. and Lai, M. -J., An Unified Convergence Theory for Newton's Type Methods for Zeros of Nonlinear Operators in Banach spaces, BIT, vol. 42 (2002) pp. 206--213 Lai, M. -J. and Schumaker, L. L., Quadrilateral Macro-Elements, SIAM Journal on Mathematical Analysis, vol. 33 (2002) pp. 1107--1116 Von Golitschek, M., Lai, M. -J. and Schumaker, L. L., Bounds for Minimal Energy Bivariate Polynomial Splines, Numerische Mathematik, vol. 93 (2002) pp. 315--331 Lai, M. -J. and Roach, D. W., Parameterizations of Univariate Orthogonal Wavelets with Short Support, Approximation Theory X: Wavelets, Splines, and Applications, Vanderbilt University Press, (2002) edited by Chui, C. K., Schumaker, L. L., Stoeckler, J. pp. 369--384 Lai, M. -J., Wenston, P. and Ying, L. A., Bivariate Splines for Exterior Biharmonic Equations, Approximation Theory X: Wavelets, Splines, and Applications, Vanderbilt University Press, (2002) edited by Chui, C. K., Schumaker, L. L., Stoeckler, J. pp. 385--404 Awanou, G. and Lai, M. -J., $C^1$ Quintic Spline Interpolation over Tetrahedral Partitions, Approximation Theory X: Wavelets, Splines, and Applications, Vanderbilt University Press, (2002) edited by Chui, C. K., Schumaker, L. L., Stoeckler, J. pp. 1--16 Lai, M. -J., Methods for Constructing Nonseparable Compactly Supported Orthonormal Wavelets, Wavelet Analysis: Twenty Year's Development, (2002) edited by D. X. Zhou, World Scientific pp. 231--251 2001 Lai, M. -J. and Schumaker, L. L., Macro-Elements and Stable Local Bases for Splines on Clough-Tocher Triangulations, Numerische Mathematik, vol. 88 (2001) pp. 105--119 Lai, M. -J. and Wenston, P., Trivariate C^1 Cubic Splines for Numerical Solution of Biharmonic Equations, Trends in Approximation Theory, Vanderbilt University Press, (2001) edited by K. Kopotun, T. Lyche, and M. Neamtu pp. 224--234 Lai, M. -J. and Roach, D. W., The Nonexistence of Bivariate Symmetric Wavelets with Short Support and Two Vanishing Moments, Trends in Approximation Theory, Vanderbilt University Press, (2001) edited by K. Kopotun, T. Lyche, and M. Neamtu pp. 213--223 2000 Lai, M. -J. and Wenston, P., On Schwarz's Domain Decomposition Methods for Elliptic Boundary Value Problems, Numerische Mathematik, vol. 84 (2000) pp. 475--495 Lai, M. -J. and Wenston, P., Bivariate Spline Method for Numerical Solution of Navier-Stokes Equations over Polygons in Stream Function Formulation, Numerical Methods for P.D.E., vol. 16 (2000) pp. 147--183 He, W. and Lai, M. -J., Examples of Bivariate Nonseparable Compactly Supported Orthonormal Continuous Wavelets, IEEE Transactions on Image Processing, vol. 9 (2000) pp. 949--953 Chui, C. K. and Lai, M. -J., Filling Polygonal Holes using $C^1$ Cubic Triangular Spline Patches, Computer Aided Geometric Design, vol. 17 (2000) pp. 297--307 Lai, M. -J., Convex Preserving Scattered Data Interpolation using Bivariate $C^1$ Cubic Splines, Journal of Computational and Applied Mathematics, vol. 119 (2000) pp. 249--258 Chui, C. K., Lai, M. -J. and Lian, J. A., Algorithms for $G\sp 1$ Connection of Multiple Parametric Bicubic NURBS Surfaces, Numerical Algorithms, vol. 23 (2000) pp. 285--313 1999 He, W. and Lai, M. -J., Construction of Bivariate Compactly Supported Biorthogonal Box Spline Wavelets with Arbitrarily High Regularities, Applied and Computational Harmonic Analysis, vol. 6 (1999) pp. 53--74 Lai, M. -J. and Schumaker, L. L., On the Approximation Power of Splines on Triangulated Quadrangulations, SIAM Journal on Numerical Analysis, vol. 36 (1999) pp. 143--159 Lai, M. -J. and Roach, D. W., Nonseparable Symmetric Wavelets with Short Support, Proceedings of SPIE Conference on Wavelet Applications in Signal and Image Processing VII, July, vol. 3813 (1999) pp. 132-146 1998 Lai, M. -J. and Schumaker, L. L., Approximation Power of Bivariate Splines, Advances in Computational Mathematics, vol. 9 (1998) pp. 251--279 Lai, M. -J. and Wenston, P., Bivariate Spline Method for Numerical Solution of Steady State Navier-Stokes Equations over Polygons in Stream Function Formulation, Advances in Computational Mathematics, New York, (1998) edited by Z. Chen, Y. Li, C. Micchelli, and Y. Xu, Marcel Dekker pp. 245--277 He, W. and Lai, M. -J., Bivariate Box Spline Wavelets in Sobolev Spaces, Wavelet Applications in Signal and Image Processing VI, proceedings of SPIE, vol. 3458 (1998) pp. 56--66 He, W. and Lai, M. -J., A New Sufficient Condition for the Orthonormality of Refineable Functions, Approximation Theory IX: Computational Aspects, Vanderbilt University Press, (1998) edited by Charles K. Chui and Larry L. Schumaker pp. 121--128 Farmer, K. W. and Lai, M. -J., Scattered Data Interpolation by C^2 Quintic Splines Using Energy Minimization, Approximation Theory IX: Computational Aspects, Vanderbilt University Press, (1998) edited by Charles K. Chui and Larry L. Schumaker pp. 47--54 Lai, M. -J. and Wenston, P., Bivariate Spline Method for Navier-Stokes Equations: Domain Decomposition Technique, Approximation Theory IX: Computational Aspects, Vanderbilt University Press, (1998) edited by Charles K. Chui and Larry L. Schumaker pp. 153--160 1997 Lai, M. -J., Geometric Interpretation of Smoothness Conditions of Triangular Polynomial Patches, Computer Aided Geometric Design, vol. 14 (1997) pp. 191--199 Lai, M. -J. and Schumaker, L. L., Scattered Data Interpolation using Piecewise Polynomials of Degree Six, SIAM Journal on Numerical Analysis, vol. 34 (1997) pp. 905--921 He, W. and Lai, M. -J., On Digital Filters Associated with Bivariate Box Spline Wavelets, Journal of Electronic Imaging, vol. 6 (1997) pp. 453--466 He, W. and Lai, M. -J., Examples of Bivariate Nonseparable Compactly Supported Orthonormal Continuous Wavelets, Wavelet Applications in Signal and Image Processing IV, proceedings of SPIE, vol. 3169 (1997) pp. 303--314 1996 Lai, M. -J., Scattered Data Interpolation and Approximation by $C^1$ Piecewise Cubic Polynomials, Computer Aided Geometric Design, vol. 13 (1996) pp. 81--88 Lai, M. -J., On the Fundamental Solutions for Multivariate Singular Interpolation, Journal of Approximation Theory and its Application, vol. 12 (1996) pp. 73--92 Lai, M. -J. and Wenston, P., On Multilevel Bases for Elliptic Boundary Value Problems, Journal of Computational and Applied Mathematics, vol. 71 (1996) pp. 95--113 Lai, M. -J., On $C^2$ Quintic Spline Functions over Triangulations of Powell-Sabin's Type, Journal of Computational and Applied Mathematics, vol. 73 (1996) pp. 135--155 Lai, M. -J., Bivariate Box Splines for Image Processing, Wavelet Applications in Signal and Image Processing IV, proceedings of SPIE, vol. 2825 (1996) pp. 474--487 1995 Lai, M. -J., On the Digital Filter Associated with Daubechies' Wavelets, IEEE Transactions on Signal Processing, vol. 43 (1995) pp. 2203--2205 Lai, M. -J., Bivariate Spline Spaces on FVS-triangulations, Approximation Theory VIII, Academic Press, (1995) edited by Chui, C. K. and Schumaker, L. L. pp. 309--316 1994 Lai, M. -J., On Computation of Battle-Lemarie's Wavelets, Mathematics of Computation, vol. 63 (1994) pp. 689--699 Lai, M. -J., On Stromberg's Spline Wavelets, Applied and Computational Harmonic Analysis, vol. 1 (1994) pp. 188--193 Lai, M. -J., Approximation Order from Bivariate $C^1$ Cubics on a Four-Directional Mesh is Full, Computer Aided Geometric Design, vol. 11 (1994) pp. 215--223 Lai, M. -J., A Matrix Approach to Computations of Various Wavelets, Proceedings of IMACS World Congress, vol. 1 (1994) pp. 284--286 1993 Lai, M. -J., Some Sufficient Conditions for Convexity of Multivariate Bernstein-Bezier Polynomials and Box Spline Surfaces, Studia Scientiarum Math. Hungarica, vol. 28 (1993) pp. 363--374 Lai, M. -J., A Serendipity Family of Locally Supported Splines in $S^2_8(\triangle)$, Journal of Approximation Theory and its Application, vol. 10 (1993) pp. 43--53 1992 Lai, M. -J., Fortran Subroutines for B-nets of Box Splines on Three and Four Directional Meshes, Numerical Algorithms, vol. 2 (1992) pp. 33--38 Chui, C. K. and Lai, M. -J., Algorithms for Generating B-nets and Graphically Displaying Box Spline Surfaces, Computer Aided Geometric Design, vol. 8 (1992) pp. 479--493 Lai, M. -J., A Characteristic Theorem of Multivariate Splines in Blossom Form, Computer Aided Geometric Design, vol. 8 (1992) pp. 513--521 Lai, M. -J., Asymptotic Formulae of Multivariate Bernstein Approximation, Journal of Approximation Theory, vol. 70 (1992) pp. 229--242 1991 Lai, M. -J., On Dual Functionals of Polynomials in B-form, Journal of Approximation Theory, vol. 67 (1991) pp. 19--37 1990 Chui, C. K. and Lai, M. -J., Multivariate Vertex Splines and Finite Elements, Journal of Approximation Theory, vol. 60 (1990) pp. 245--343 Chui, C. K. and Lai, M. -J., On Bivariate Super Vertex Splines, Constructive Approximation, vol. 6 (1990) pp. 399--419 1989 Lai, M. -J., A Remark on Integer Translates of a Box Spline, Journal of Approximation Theory and its Application, vol. 5 (1989) pp. 97--104 Lai, M. -J., On Construction of Bivariate and Triavariate Vertex Splines, Texas AM University, (1989) pp. Dept. of Mathematics 1988 Chen, G. R., Chui, C. K. and Lai, M. -J., Construction of Real-Time Spline Quasi-Interpolation Scheme, Journal of Approximation Theory and its Application, vol. 4 (1988) pp. 61--75 1987 Chui, C. K. and Lai, M. -J., Computation of Box Splines and B-splines on Triangulations of Nonuniform Rectangular Partitions, Journal of Approximation Theory and its Application, vol. 3-4 (1987) pp. 37--62 Chui, C. K. and Lai, M. -J., Multivariate Analog of Marsden's Identity and a Quasi-Interpolation Scheme, Constructive Approximation, vol. 3 (1987) pp. 111--122 Chui, C. K. and Lai, M. -J., VanderMonde Determinants and Lagrange Interpolation in R^s, Nonlinear and Convex analysis, Marcel Dekker, (1987) edited by B.L.Lin and S.Simons pp. 23--35 Chui, C. K. and Lai, M. -J., On Multivariate Vertex Splines and Applications, Topics in Multivariate Approximation, Academic Press, (1987) edited by Chui, C.K., L.L. Schumaker, and F. Utreras pp. 19--36 1986 Lai, M. -J. and Wang, X. H., On Multivariate Newtonian Interpolation, Scientia Sinica, vol. 29 (1986) pp. 23--32 1985 Lai, M. -J., Exact Error Bounds for Cubic Birkhoff Spline Interpolation, Numerical Math. J. Chinese Univ., vol. 7 (1985) pp. 369--372 Chui, C. K. and Lai, M. -J., On Bivariate Vertex Splines, Multivariate Approximation Theory III, Birkhauser, (1985) edited by W.Schempp and K.Zeller pp. 84--115 1984 Lai, M. -J., On Estimations for the Exact Bounds of the Coefficients of Approximation by Cubic Spline Interpolation, Math. Numer. Sinica, vol. 6 (1984) pp. 105--108 Lai, M. -J. and Wang, X. H., A Note to the Remainder of a Multivariate Interpolation Polynomial, Journal of Approximation Theory and its Application, vol. 1 (1984) pp. 57--63 Lai, M. -J. and Feng, G. J., On the Uniform Convergence of the Birkhoff Interpolation with Two Points, Math. Numer. Sinica, vol. 6 (1984) pp. 222--224
