On evaluating higher-order derivatives of the QR decomposition of tall matrices with full column rank in forward and reverse mode algorithmic differentiation

DOI10.1080/10556788.2011.610454zbMath1242.65048OpenAlexW2143934028MaRDI QIDQ2885486

Lutz Lehmann, René Lamour, Sebastian F. Walter

Publication date: 23 May 2012

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556788.2011.610454

zbMATH Keywords

algorithmsautomatic differentiationnull spacealgorithmic differentiationQR decompositionsforward/reverse modehigher-order derivative evaluationunivariate Taylor polynomial arithmetic

Mathematics Subject Classification ID

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

Related Items (2)

A Grassmann manifold handbook: basic geometry and computational aspects ⋮ Projector based integration of DAEs with the Taylor series method using automatic differentiation

Uses Software

• NumPy

Cites Work

• Evaluating Derivatives
• MultiStage Approaches for Optimal Offline Checkpointing
• A mathematical view of automatic differentiation
• Evaluating higher derivative tensors by forward propagation of univariate Taylor series
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