In this paper, we give a regularized directional derivative-based Newton method for solving the inverse singular value problem. The proposed method is also globalized by employing the directional derivative-based Wolfe line search conditions. Under some mild assumptions, The global and quadratic convergence of our method is established. To improve the practical effectiveness, we also propose a hybrid method for solving the inverse singular value problem. We show that the hybrid method converges locally quadratically and globally in the sense that a stationary point of a merit function for the inverse singular value problem is computed. Numerical tests demonstrate that the proposed hybrid method is very effective for solving the inverse singular value problem with distinct and multiple singular values.

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The asymmetric hydroalkylation of racemic allylic alcohols has been developed for the synthesis of chiral amino acid derivatives with two remote chiral centers by borrowing hydrogen catalysis. The stereoselectivities are controlled by a single chiral Ru catalyst via a dynamic kinetic asymmetric transformation process and an interesting diastereoselectivity amplification process of the product. The method could be used for the synthesis of several types of biologically important molecules, including stereodivergent synthesis of chiral pyrrolidine derivatives.

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