Eigenvalue bounds of the shift-splitting preconditioned singular nonsymmetric saddle-point matrices

Eigenvalue bounds of the shift-splitting preconditioned singular nonsymmetric saddle-point matrices

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Abstract For singular nonsymmetric saddle-point problems, a shift-splitting preconditioner was studied in (Appl.Math.Comput.269:947-955, 2015).

To further show the efficiency of the shift-splitting Apron preconditioner, we provide eigenvalue bounds for the nonzero eigenvalues of the shift-splitting preconditioned singular nonsymmetric saddle-point matrices.For real parts of the eigenvalues, the bound is provided by valid inequalities.For eigenvalues having nonzero imaginary parts, the bound Samsung RS52N3313WW No Frost Side-by-side Fridge Freezer With Non-pl is a combination of two inequalities proving their clustering in a confined region of the complex plane.Finally, two numerical examples are presented to verify the theoretical results.