Preconditioning

A hundred iterations

Lurking in every giant problem are many problems of smaller size. In the large-scale seismic imaging problem lie problems of velocity estimation, multiple-reflection elimination, and many more.

Envision a large problem feasible in a hundred iterations. Many of my colleagues work on such problems. Maybe half would also use exotic parallel computer architectures. Those with ample energy and intellectual capacity to tackle such machines are rewarded by speed-up factors of 10 to a 100, rewarded also by a diverse population of industries hiring. This skill stays in demand because new architectures rapidly obsolete earlier generations. The other half, people like me, have the luxury of software (like in this book) decaying at a slower pace, leaving us needed time to tune our imaginations to extracting the structure of more complex problems.

It is a giant leap of faith that we can accomplish something of value with a mere hundred iterations in a task that theoretically demands quadrillions. Experience shows that we often do, and we do so by experimenting with ``intuitive'' methods. The first, I shall call ``faking the epsilon.''

Preconditioning