Iterative Methods for Solving Partial Difference Equations of Elliptic Type

  • DAVID YOUNGO
  • Published 2010

Abstract

Conditions (1.2) were formulated by Geiringer [4, p. 379](2). Evidently these conditions imply that a^^O (i=l, 2, • • • , TV). It is easy to show by methods similar to those used in [4, pp. 379-381] that the determinant of the matrix A = (a-.-.y) does not vanish. Moreover, if the matrix A*=ia*f) is symmetric, where aj = flj,%ßi,j/\ a.-.ii| (i, 7=1, 2, • • • , TV), then A * is positive definite. For if X is a nonpositive real number, then the matrix A*—X7, where 7 is the identity matrix, also satisfies (1.2) and hence its determinant cannot vanish. Therefore all eigenvalues of A* are positive, and A* is positive definite. On the other hand if A* is positive definite then ai.,-^0 (¿=1,2, • • -,TV). We shall be concerned with effective methods for obtaining numerical solu-

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@inproceedings{YOUNGO2010IterativeMF, title={Iterative Methods for Solving Partial Difference Equations of Elliptic Type}, author={DAVID YOUNGO}, year={2010} }