A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical im...A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.展开更多
Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion ...Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjugate gradient method. For the constant-coefficient second-order hyperbolic equaions with initial and Dirichlet boundary conditions,we prove that the conditionnumber of the preconditioned interface system is bounded by 2+x2 2+0.46x2 where x is the quo-tient between the lime and space steps. Such condition number produces a convergence rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equations.展开更多
The solution transformations and properties of the R-matrices for two-component systems uner these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin's formalism.F...The solution transformations and properties of the R-matrices for two-component systems uner these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin's formalism.For those R-matrices with all required properties,the effects of solution transformations to the six- and eight-vertex systems with open boundary conditions are discussed.These effects can be one of the following types: The Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.展开更多
A numerical solution of the quadratic matrix equations associated with a nonsingular M-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingula...A numerical solution of the quadratic matrix equations associated with a nonsingular M-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingular M-matrix solution of the quadratic matrix equations is developed, and its corresponding theory is given. Some numerical examples are provided to show the efficiency of the new method.展开更多
文摘A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.
文摘Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjugate gradient method. For the constant-coefficient second-order hyperbolic equaions with initial and Dirichlet boundary conditions,we prove that the conditionnumber of the preconditioned interface system is bounded by 2+x2 2+0.46x2 where x is the quo-tient between the lime and space steps. Such condition number produces a convergence rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equations.
基金Natural Science Foundation of Science and Technology Committee of Henan Proviuce，河南师范大学校科研和教改项目
文摘The solution transformations and properties of the R-matrices for two-component systems uner these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin's formalism.For those R-matrices with all required properties,the effects of solution transformations to the six- and eight-vertex systems with open boundary conditions are discussed.These effects can be one of the following types: The Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.
基金This work was supported by the National Natural Science Foundation （No.11171337）, P. R. China.
文摘A numerical solution of the quadratic matrix equations associated with a nonsingular M-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingular M-matrix solution of the quadratic matrix equations is developed, and its corresponding theory is given. Some numerical examples are provided to show the efficiency of the new method.
