Philipp H. W. Hoffmann

activity

20112015

most citedA Hitchhiker's Guide to Automatic Differentiation

31 citations · 66 across the 4 of their papers we have counts for

collaborators

4 papers

math.FA2015

A note on operator tuples which are $(m, p)$ -isometric as well as $(μ, \infty)$ -isometric

Philipp H. W. Hoffmann

We show that if a tuple of commuting, bounded linear operators $(T_{1}, ..., T_{d}) \in B (X)^{d}$ is both an $(m, p)$ -isometry and a $(μ, \infty)$ -isometry, then the tuple $(T_1^m,...,T_d^m)…

math.NA2014★ 31 cited

A Hitchhiker's Guide to Automatic Differentiation

Philipp H. W. Hoffmann

This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode o…

math.FA2012★ 14 cited

$(m, p)$ -isometric and $(m, \infty)$ -isometric operator tuples on normed spaces

Philipp H. W. Hoffmann, Michael Mackey

We generalize the notion of $m$ -isometric operator tuples on Hilbert spaces in a natural way to normed spaces. This is done by defining a tuple analogue of $(m, p)$ -isometric operat…

math.FA2011★ 21 cited

On the second parameter of an $(m, p)$ -isometry

Philipp Hoffmann, Michael Mackey, Mícheál Ó Searcóid

A bounded linear operator $T$ on a Banach space $X$ is called an $(m, p)$ -isometry if it satisfies the equation \sum_{k=0}^{m}(-1)^{k} {m \choose k}\|T^{k}x\|^{p} = 0 $, f or a l l$ x…

A note on operator tuples which are (m,p)-isometric as well as (μ,∞)-isometric

A Hitchhiker's Guide to Automatic Differentiation

(m,p)-isometric and (m,∞)-isometric operator tuples on normed spaces

On the second parameter of an (m,p)-isometry

A note on operator tuples which are $(m, p)$ -isometric as well as $(μ, \infty)$ -isometric

$(m, p)$ -isometric and $(m, \infty)$ -isometric operator tuples on normed spaces

On the second parameter of an $(m, p)$ -isometry