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On evaluating higher-order derivatives of the QR decomposition of tall matrices with full column rank in forward and reverse mode algorithmic differentiation. (English) Zbl 1242.65048

Summary: We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions of tall matrices with full column rank. The approach is a combination of univariate Taylor polynomial arithmetic and matrix calculus in the (combined) forward/reverse mode of algorithmic differentiation. Explicit algorithms are derived and presented in an accessible form.

MSC:

65D25 Numerical differentiation
12E05 Polynomials in general fields (irreducibility, etc.)
58C15 Implicit function theorems; global Newton methods on manifolds
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F25 Orthogonalization in numerical linear algebra
65F05 Direct numerical methods for linear systems and matrix inversion

Software:

NumPy
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References:

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