Functions of Matrices

By W. Steeb, Y. Hardy. 2006

160 citations recorded by the source corpus.

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On the Bures–Wasserstein distance between positive definite matrices (2017, background): “See [18] for a brief and [16] for an expansive discussion.”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, methodology): “Borrowing notation from the theory of matrix functions [38], we can also write (12) and (13) as f out = ˆ h ( Ł ) f in , where The basic graph spectral ﬁltering (12) can be used to implement discrete versions of well-known continuous ﬁltering techniques such as Gaussian smoothing, bilateral…”
Vertex-Frequency Analysis on Graphs (2013, methodology): “…Laplacian eigenvectors, we deﬁne a generalized convolution of signals f, g ∈ R N on a graph by Using notation from the theory of matrix functions [23], we can also write the generalized convolution as Proposition 1: The generalized convolution product deﬁned in (16) satisﬁes the following…”
Accelerated filtering on graphs using Lanczos method (2015, background): “In terms of matrix functions [11], the relation (1) can be compactly expressed as s ′ = g ( ) s with g ( ) := Ug (Λ) U ∗ .”