Nonlinear Difference Equations and Gauss-Seidel Type Iterative Methods

@article{Ortega1966NonlinearDE,
  title={Nonlinear Difference Equations and Gauss-Seidel Type Iterative Methods},
  author={James M. Ortega and Maxine L. Rockoff},
  journal={SIAM Journal on Numerical Analysis},
  year={1966},
  volume={3},
  pages={497-513}
}
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References

SHOWING 1-2 OF 2 REFERENCES

Matrix Iterative Analysis

Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and