Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits

2015 ◽  
Vol 22 (1-3) ◽  
pp. 1102-1133 ◽  
Author(s):  
J.D. Mireles James
Keyword(s):  
Linear Approximation ◽  
Error Bounds ◽  
Computer Assisted ◽  
Connecting Orbits ◽  
Stable Manifolds ◽  
Higher Dimensional

scholarly journals Computing (Un)stable Manifolds with Validated Error Bounds: Non-resonant and Resonant Spectra

2016 ◽  
Vol 26 (4) ◽  
pp. 1055-1095 ◽  
Author(s):  
Jan Bouwe van den Berg ◽  
Jason D. Mireles James ◽  
Christian Reinhardt
Keyword(s):  
Error Bounds ◽  
Stable Manifolds ◽  
Validated Error Bounds

scholarly journals Subdivision Depth Computation for Tensor Productn-Ary Volumetric Models

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Ghulam Mustafa ◽  
Muhammad Sadiq Hashmi
Keyword(s):  
Tensor Product ◽  
Error Bounds ◽  
Error Control ◽  
Computational Formula ◽  
Evaluation Technique ◽  
Volumetric Models ◽  
Higher Dimensional ◽  
Special Cases ◽  
Subdivision Depth ◽  
Control Tool

We offer computational formula of subdivision depth for tensor productn-ary (n⩾2) volumetric models based on error bound evaluation technique. This formula provides and error control tool in subdivision schemes over regular hexahedron lattice in higher-dimensional spaces. Moreover, the error bounds of Mustafa et al. (2006) are special cases of our bounds.

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