Preface

Summary

My first contact with ill-conditioned inverse problems was while flying to the 1977 Australian Applied Mathematics Conference at Terrigal, NSW. By chance, I was seated next to Bob Anderssen, who showed me his recent report on regularisation expressed in terms of Fredholm integrals.

Ill-conditioned problems have now dominated the largest part of my scientific career. However, back in 1977, my (private) reaction to Bob's work was ‘why would any reasonable person want to work on such perversely difficult problems?’. The answer, ‘that this is the form in which we get most of our information about the real world’, completely escaped me. In any case, my idealised modelling of phase transitions in lattice systems was seemingly only loosely related to the real world – even my percolation modelling of bubble trapping lay many years in the future.

Two jobs later, I had left mathematical physics as a career and was working for CSIRO modelling the carbon cycle. In particular, I was trying to calibrate our model. My attempts at finding a best-fit parameter set were thrashing around in some poorly defined subspace, when a vague memory stirred. It took me about two days to find Bob's report again and start to realise what I was up against and what I should do about it.

One important point is that what Bob gave me was a technical report. This genre is much-maligned as ‘grey-literature’. It can, however, have the advantage of telling ‘the truth’ and ‘the whole truth’, even if the lack of anonymous peer review means occasional failures of ‘nothing but the truth’.