Derivative operations on matrices

Vetter, W.

doi:10.1109/tac.1970.1099409

Cited by 78 publications

(15 citation statements)

References 2 publications

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“…Brewer [2] (Eq. 23) obtained a different version of (41) using Vetter's [34] matrix derivative. Using the Magnus and Neudecker matrix derivative, McCrorie [16] and Chen and Zadrozny [4] obtained a special case of (41) assuming R = D.…”

Section: Derivatives Of Matrix Exponentialsmentioning

confidence: 99%

Recursions for the MMPP Score Vector and Observed Information Matrix

Willy¹,

Roberts²,

Mazzuchi

et al. 2010

Stochastic Models

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Exact forward recursions for the score vector and observed information matrix of the Markov-modulated Poisson process (MMPP) are developed. The recursions are motivated by similar recursions developed for hidden Markov models by Lystig and Hughes who extended earlier work by LeGland and Mèvel. Explicit expressions for the first derivative and Hessian of the MMPP transition density matrix are developed and coupled with the recursions. The recursions are implemented and applied to confidence interval estimation in a simulation study.

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Section: Derivatives Of Matrix Exponentialsmentioning

confidence: 99%

Recursions for the MMPP Score Vector and Observed Information Matrix

Willy¹,

Roberts²,

Mazzuchi

et al. 2010

Stochastic Models

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show abstract

“…The chain rule for the derivative of a matrix Z = Y (X) with respect to a matrix X, with X ∈ m×n , Y ∈ n×r , Z ∈ p×q , takes the form [6, p. 88], [14] (3.12)…”

Section: Approximate Inverse Mappings and Error Boundsmentioning

confidence: 99%

Approximations and error bounds for computing the inverse mapping

Jódar

Ponsoda

Rodríguez

1997

Applications of Mathematics

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“…The Kronecker product is very useful in the field of matrix calculus (Graham 1981 xT Fact (Vetter 1970(Vetter ,1971: Using the definition of Kronecker product and derivative operations on matrices, Taylor's formula can be expressed by In this section, our main results will be given. If f(x,u) has an equilibrium point, without loss of generality, we can assume that f(0,0) =0;…”

Section: Preliminariesmentioning

confidence: 99%