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The paper presents two numerical methods for solving the error minimization problems and illustrates the methodology in several numerical examples in the areas of uncertainty quantification, reliability engineering, and financial risk management.
These are applied as 'a single iteration of a multigrid cycle comprised of manipulating the error by the application of relaxation method, fixing the residuals on the coarse grid level, solving the error equation on the coarse grid and adjusting the correction of coarse grid up to the fine grid level'.
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Unlike [9] which designs list decoding with a purpose to solve the error-correcting problem in random network coding, [8, 23, 24, 34, 35] are not designed for solving the error-correcting problem in random network coding.
Moreover, it properly solves the error accumulation problem.
The experiments show our scheme can solve the error spread problem in random network coding.
However, none of the existing works solved the error spread problem in random network coding.
The rank code or the subspace code are the best cure methods to solve the error spread in the random network coding at present.
It is derived to solve the error locator and evaluator polynomials simultaneously without performing the operations of polynomial division and field element inversion.
Therefore, it is clear that in the 50-m SI-POF channel, using RSSE (2,1) equalizer can solve the error propagation problem in classical DFE equalizers.
Whether the rank code or the subspace code, they just can solve the error spread problem in the random network where the number of original error is less than C/2.
Based on the above description, the existing methods to solve the error-correcting problem in network coding are divided into six categories.
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