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- V. Baramidze, M. J. Lai, C. K. Shum
- SIAM J. Scientific Computing
- 2006

We study minimal energy interpolation and discrete and penalized least squares approximation problems on the unit sphere using nonhomogeneous spherical splines. Several numerical experiments are conducted to compare approximating properties of homogeneous and nonhomogeneous splines. Our numerical experiments show that nonhomogeneous splines have certain… (More)

The convergence of the minimal energy interpolatory splines on the unit sphere is studied in this paper. An upper bound on the difference between a sufficiently smooth function and its interpolatory spherical spline in the infinity norm is given. The error bound is expressed in terms of a second order spherical Sobolev-type seminorm of the original… (More)

- Ming-Jun Lai, M. J. Lai
- 2007

Methods for scattered data fitting using multivariate splines will be surveyed in this paper. Existence, uniqueness, and computational algorithms for these methods, as well as their approximation properties will be discussed. Some applications of multivariate splines for data fitting will be briefly explained. Some new research initiatives of scattered data… (More)

We use splines on spherical triangulations to approximate the solution of a second order elliptic PDE over the unit sphere. We establish existence and uniqueness of weak solutions in spherical spline spaces and estimate convergence of the spline approximations. We present a computational algorithm and summarize numerical results on convergence rates. §

- Victoria Baramidze, M. J. Lai, +5 authors Jun Lai
- 2005

We study properties of spherical Bernstein-Bézier splines. Algorithms for practical implementation of the global splines are presented for a homogeneous case as well as a non-homogeneous. Error bounds are derived for the global splines in terms of Sobolev type spherical semi-norms. Multiple star technique is studied for the minimal energy interpolation… (More)

- Okkyung Cho, Ming-Jun Lai, M. J. Lai
- 2006

Abstract. We continue the study of constructing compactly supported orthonormal B-spline wavelets originated by T.N.T. Goodman. We simplify his constructive steps for compactly supported orthonormal scaling functions and provide an inductive method for constructing compactly supported orthonormal wavelets. Three examples of compactly supported orthonormal… (More)

- Jason Y. Zhang, Cemal Cem Tasan, M. J. Lai, A-C Dippel, Dierk Raabe
- Nature communications
- 2017

The most efficient way to tune microstructures and mechanical properties of metallic alloys lies in designing and using athermal phase transformations. Examples are shape memory alloys and high strength steels, which together stand for 1,500 million tons annual production. In these materials, martensite formation and mechanical twinning are tuned via… (More)

- V. Baramidze, M. J. Lai
- 2004

Trivariate splines solve a special case of scattered data interpolation problem in the volume bounded by two concentric spheres. A triangulation ∆ of the unit sphere S is constructed based on the vertex set V. Given a partition P of the interval [1, R], let Sτ×ρ σ×δ be the space of the spherical splines of degree σ and smoothness τ over ∆ tensored with the… (More)

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