Schwarz Iterations for Symmetric Positive Semidefinite Problems | Zendy

Reinhard Nabben | Zendy; Daniel B. Szyld | Zendy

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Schwarz Iterations for Symmetric Positive Semidefinite Problems

Author(s) -

Reinhard Nabben,

Daniel B. Szyld

Publication year - 2006

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/050644203

Subject(s) - mathematics , positive definite matrix , block matrix , invertible matrix , multiplicative function , matrix (chemical analysis) , boundary value problem , partial differential equation , mathematical analysis , pure mathematics , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material

Convergence properties of additive and multiplicative Schwarz iterations for solving linear systems of equations with a symmetric positive semidefinite matrix are analyzed. The analysis presented applies to matrices whose principal submatrices are nonsingular, i.e., positive definite. These matrices appear in discretizations of some elliptic partial differential equations, e.g., those with Neumann or periodic boundary conditions.

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