We consider the approximation of manifold-valued functions by embedding the manifold into a higher dimensional space, applying a vector-valued approximation operator and projecting the resulting vector back to the manifold. It is well known that the approximation error for manifold-valued functions is close to the approximation error for vector-valued functions. This is not true anymore if we consider the derivatives of such functions. In our paper we give pre-asymptotic error bounds for the approximation of the derivative of manifold-valued function. In particular, we provide explicit constants that depend on the reach of the embedded manifold.
Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential
GIK Institute of Engineering Sciences & Technology（GIK工程科学与技术学院）；Università dell’Insubria（因斯布鲁克大学）；Uppsala University（乌普萨拉大学）；Bacha Khan University（巴查汗大学）；University of Milano - Bicocca（米兰比可卡大学）
An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport
Memorial Sloan Kettering Cancer Center（纪念斯隆-凯特琳癌症中心）；University British Columbia（不列颠哥伦比亚大学）；Lund University（隆德大学）；University of California, Irvine（加州大学尔湾分校）；Stony Brook University（石溪大学）
