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This is a survey paper on applications of mathematics of semirings tonumerical analysis and computing. Concepts of universal algorithm and genericprogram are discussed. Relations between these concepts and mathematics ofsemirings are examined. A very brief introduction to mathematics of semirings(including idempotent and tropical mathematics) is presented. Concreteapplications to optimization problems, idempotent linear algebra and intervalanalysis are indicated. It is known that some nonlinear problems (andespecially optimization problems) become linear over appropriate semirings withidempotent addition (the so-called idempotent superposition principle). Thislinearity over semirings is convenient for parallel computations.

Universal algorithms, mathematics of semirings and parallel computations