For large sparse system of linear equations with the coefficient matrix with a dominant indefinite symmetric part, we present a class of splitting minimal resid- ual method, briefly called as SMINRES-method, by making...
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For large sparse system of linear equations with the coefficient matrix with a dominant indefinite symmetric part, we present a class of splitting minimal resid- ual method, briefly called as SMINRES-method, by making use of the inner/outer iteration technique. The SMINRES-method is established by first transforming the linear system into an equivalent fixed-point problem based on the symmetric/skew- symmetric splitting of the coefficient matrix, and then utilizing the minimal resid- ual (MINRES) method as the inner iterate process to get a new approximation to the original system of linear equations at each of the outer iteration step. The MINRES can be replaced by a preconditioned MINRES (PMINRES) at the inner iterate of the SMINRES method, which resulting in the so-called preconditioned splitting minimal residual (PSMINRES) method. Under suitable conditions, we prove the convergence and derive the residual estimates of the new SMINRES and PSMINRES methods. Computations show that numerical behaviours of the SMIN- RES as well as its symmetric Gauss-Seidel (SGS) iteration preconditioned variant, SGS-SMINRES, are superior to those of some standard Krylov subspace meth- ods such as CGS, CMRES and their unsymmetric Gauss-Seidel (UGS) iteration preconditioned variants UGS-CGS and UGS-GMRES.
By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = D under the restriction that the solution matrix ...
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By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = D under the restriction that the solution matrix ∈ Rn×n is bisymmetric, where A ∈Rn×m and D ∈Rm×m are given matrices.
In this paper we discuss the natural boundary element method for harmonic equation in an exterior elliptic domain. By studying the properties of the natural integral operator and the Poisson integral operator, we deve...
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In this paper we discuss the natural boundary element method for harmonic equation in an exterior elliptic domain. By studying the properties of the natural integral operator and the Poisson integral operator, we develop a numerical method to solve the natural integral equation. We also devise a fast algorithm for the solution of the corresponding system of linear equations. Finally we present some numerical results.
The paper presents a posteriori error estimate of FD-SD method for one- dimension time-dependent convection- dominated diffusion equation 5 which can be used to adjust space mesh. Some numerical results and an algorit...
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The paper presents a posteriori error estimate of FD-SD method for one- dimension time-dependent convection- dominated diffusion equation 5 which can be used to adjust space mesh. Some numerical results and an algorithm of adaptive finite element method based on this a posteriori error estimate are given.
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