Riemannian Newton-CG methods for constructing a positive doubly stochastic matrix from spectral data
نویسندگان
چکیده
منابع مشابه
Matrix Eigen-decomposition via Doubly Stochastic Riemannian Optimization: Supplementary Material
Preparation First, based on the definitions of A t , Y t , ˜ Z t and Z t , we can write g t = G(s t , r t , X t) = p −1 st p −1 rt (I − X t X ⊤ t)(E st ⊙ A)(E ·rt ⊙ X) = (I − X t X ⊤ t)A t Y t. Then from (6), we have X t+1 = X t + α t g t W t − α 2 t 2 X t g ⊤ t g t W t. Since W t = (I + α 2 t 4 g ⊤ t g t) −1 = I − α 2 t 4 g ⊤ t g t + O(α 4 t), we get X t+1 = X t + α t A t Y t − α t X t X ⊤ t A...
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ژورنال
عنوان ژورنال: Inverse Problems
سال: 2020
ISSN: 0266-5611,1361-6420
DOI: 10.1088/1361-6420/abbac5