This is a survey paper on applications of mathematics of semirings to
numerical analysis and computing. Concepts of universal algorithm and generic
program are discussed. Relations between these concepts and mathematics of
semirings are examined. A very brief introduction to mathematics of semirings
(including idempotent and tropical mathematics) is presented. Concrete
applications to optimization problems, idempotent linear algebra and interval
analysis are indicated. It is known that some nonlinear problems (and
especially optimization problems) become linear over appropriate semirings with
idempotent addition (the so-called idempotent superposition principle). This
linearity over semirings is convenient for parallel computations.