Projections methods for oversized linear algebra problems

Everybody who has some experience in doing mathematics knows that di mensional reduction and projection are useful tools to confront problems that are too complicated to solve without any simplication Who hasnt occasion ally but notwithstanding timidly suggested that perhaps it would be a good idea to study the simple onedimensional case rst before trying to understand the realworld threedimensional problem Apparently it is a widespread faith that such simplications will not damage the essential mathematical or physical truth that is hidden in the original problem But is this faith founded Re gardless of the answer one should realize that in many applications there is no plausible alternative so it would be unfair to judge too harshly on those who solve reduced problems and with due mathematical care formulate interesting and strong theorems and hypotheses on the full problem Among them are the people from the eld of numerical linear algebra