Best Least Squares Solutions to Finite Difference Equations Using the Generalized Inverse and Tensor Product Methods

ABSTRACT

A direct (noniterative) method for solving some singular systems of equations arising from finite difference approximations to partial differential equations is developed. The Moore-Penrose generalized inverse of some large tensor product matrices is expressed in terms of smaller matrices. Some techniques are given to improve computational efficiency.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Finite difference methods

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Least squares methods

General Terms:
Theory, Verification