FFT-Based Methods for Discrete-Time Matrix Convolutions with Applications
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Algebraic and FFT-Based Methods for Discrete-Time Matrix Convolutions with Applications to Semi-Markov Models
arXiv:2605.30379v2 Announce Type: replace Abstract: We study the convolution product of matrix-valued sequences and its role in the computation of Markov renewal equations. Explicit representations and recursive formulae for the convolutional inverse are derived and used to construct FFT-accelerated convolution and Newton-type inversion schemes, together with a Gauss--Jordan alternative in truncated power-series rings. The proposed framework is also applied to discrete approximations of...
Algebraic and FFT-Based Methods for Discrete-Time Matrix Convolutions with Applications to Semi-Markov Models
arXiv:2605.30379v1 Announce Type: new Abstract: We study the convolution product of matrix-valued sequences and its role in the computation of Markov renewal equations. Explicit representations and recursive formulae for the convolutional inverse are derived and used to construct FFT-accelerated convolution and Newton-type inversion schemes, together with a Gauss--Jordan alternative in truncated power-series rings. The proposed framework is also applied to discrete approximations of matrix...