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Application of the Ergodic Algorithm for Solving Nonlinear Equations and Tridiagonal Linear Equations

Excerpt

An ergodic algorithm was proposed for solving a class of nonlinear equations and a new algorithm was proposed for solving tridiagonal linear equations. By traversing a single variable, the ergodic algorithm for nonlinear equations can find all real solutions in the specified interval and avoid the iteration divergence. In the algorithm for tridiagonal linear equations, the equations were turned into a linear equation with only one variable. Compared to the computation time by the chasing algorithm for tridiagonal linear equations, the time by this new algorithm is reduced by 40%∼50% according to simulation results when the tridiagonal matrix dimension is less than 30000.

  • Abstract
  • Keywords
  • Introduction
  • Solving Nonlinear Equations by the Ergodic Algorithm
  • Application of the Ergodic Algorithm for Solving Tridiagonal Linear Equations
  • Conclusions
  • References

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