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===Simultaneous solutions===
Simultaneous solutions are based on solving for both {{math|X}} and {{math|Z}} at the same time (rather than basing the solution of one part off of the other as in separable solutions), propagation of error is significantly reduced.<ref name="dual-quaternions">Algo Li, et al. [https://web.archive.org/web/20200209164546/https://pdfs.semanticscholar.org/225d/e4ea2d3f18b7743bfeabf925fa603fc47bcb.pdf "Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product."] International Journal of the Physical Sciences Vol. 5(10), pp. 1530-1536, 4 September 2010.</ref> By formulating the matrices as [[dual quaternion]]s, it is possible to get a linear equation by which {{math|X}} is solvable in a linear format.<ref name="tsapps"/> An alternative way applies the [[least squares|least-squares method]] to the [[Kronecker product]] of the matrices {{math|A⊗B}}. As confirmed by experimental results, simultaneous solutions have less error than separable quaternion solutions.<ref name="dual-quaternions"/>
===Iterative solutions===
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