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.
This paper is interested in a system of conservation laws with a stiff relaxation term arised in viscoelasticity. The properties of a class of fully implicit finite difference methods approximating this system are ana...
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This paper is interested in a system of conservation laws with a stiff relaxation term arised in viscoelasticity. The properties of a class of fully implicit finite difference methods approximating this system are analyzed, which include maximum principles, bounds on the total variation, Ll-bounds, and L1-continuity estimates in term of some conserved physical quantity and this characteristic variables generated by difference schemes with proper initial data. These estimates are necessary for the existence of a bounded-total variation (BV) solution. Furthermore, we show that numerical entropy inequalities for some convex entropy pairs of the fully system hold.
Presents a study which applied the overlapping domain decomposition method based on the natural boundary reduction to solve the boundary value problem of harmonic equation over domain. Methods to solve boundary value ...
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Presents a study which applied the overlapping domain decomposition method based on the natural boundary reduction to solve the boundary value problem of harmonic equation over domain. Methods to solve boundary value problems; Contraction factor for the domain; Results.
Constructs a Fourier-Legendre pseudospectral scheme for Navier-Stokes equations with semi-periodic boundary condition. Equation of the scheme; Estimation of errors; Numerical results.
Constructs a Fourier-Legendre pseudospectral scheme for Navier-Stokes equations with semi-periodic boundary condition. Equation of the scheme; Estimation of errors; Numerical results.
In this paper, we solve a problem on the existence of conjugate symplecticity of linear multi-step methods (LMSM), the negative result is obtained. [ABSTRACT FROM AUTHOR]
In this paper, we solve a problem on the existence of conjugate symplecticity of linear multi-step methods (LMSM), the negative result is obtained. [ABSTRACT FROM AUTHOR]
In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite...
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In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived. [ABSTRACT FROM AUTHOR]
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