136 citations · 436 across the 9 of their papers we have counts for
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math.GM2014★ 129 cited
The Theory of Quaternion Matrix Derivatives
Dongpo Xu, Danilo P. Mandic
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped wi…
math.GM2014★ 125 cited
Quaternion Derivatives: The GHR Calculus
Dongpo Xu, Cyrus Jahanchahi, Clive C. Took +1
Quaternion derivatives in the mathematical literature are typically defined only for analytic (regular) functions. However, in engineering problems, functions of interest are often…
math.NA2014★ 136 cited
Quaternion Gradient and Hessian
Dongpo Xu, Danilo P. Mandic
The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions often requi…