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. Author manuscript; available in PMC: 2024 Nov 1.

Published in final edited form as: IEEE Robot Autom Lett. 2023 Sep 22;8(11):7495–7502. doi: 10.1109/lra.2023.3318115

TABLE III.

Computational Efficiency for the Hessian

	FD of Jacobian			Derivative Propagation

ODE solver	ode45	ode23	ode113	ode45	ode23	ode113

Time (s)	0.498	0.320	0.293	0.159	0.133	0.125
ODE calls	1645	908	953	95	67	54
No. × (10⁶)	3.06	1.69	1.77	1.43	1.01	0.812
No. + (10⁶)	1.18	0.651	0.683	0.571	0.402	0.325
Error (%)	0	3.82	1.90	0.0526	1.23	0.649