The simplifications of band-structure calculations which are now referred to as linear methods were introduced by Ole K. Andersen almost ten years ago. Since then these ideas have been taken up by several workers in the field and translated into computer programmes that generate the band structure of almost any material. As a result, running times on computers have been cut by orders of magnitude. One of the strong motivations behind the original proposal was a desire to give the conventional methods' a physically meaningful content which could be understood even by the non-specialist....