In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign...In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign pattern matrix (or sign pattern).For a re-al matrix B,by sgn (B) we mean the sign pattern matrix in which each positive (respec-tively,negative,zero) entry of B is replaced by+(respectively,-,0).If A is an展开更多
In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied...In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied entrywise.展开更多
Main resultsTheorem 1 Let A be symmetric positive semidefinite.Let (?) be a diagonally compen-sated reduced matrix of A and Let (?)=σI+(?)(σ】0) be a modiffication(Stieltjes) matrixof (?).Let the splitting (?)=M-(?)...Main resultsTheorem 1 Let A be symmetric positive semidefinite.Let (?) be a diagonally compen-sated reduced matrix of A and Let (?)=σI+(?)(σ】0) be a modiffication(Stieltjes) matrixof (?).Let the splitting (?)=M-(?) be regular and M=F-G be weak regular,where M andF are symmetric positive definite matrices.Then the resulting two-stage method corre-sponding to the diagonally compensated reduced splitting A=M-N and inner splitting M=F-G is convergent for any number μ≥1 of inner iterations.Furthermore,the展开更多
In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deflation to drop converged linear systems using ...In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deflation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saunders’ MINRES method for iterative solution of symmetric linear systems, and describe important implementation details. We establish a relationship between the block Lanczos algorithm and block MINRES algorithm, and compare the numerical performance of the Lanczos algorithm and MINRES method for symmetric linear systems applied to a sequence of right hand sides with that of the block Lanczos algorithm and block MINRES algorithm for multiple linear systems simultaneously.[WT5,5”HZ]展开更多
In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given se...In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.展开更多
constant whenever （x, y）∈Rk. This constant is denoted by p<sub>ij</sub><sup>k</sup>. Then we call X=(X,{Ri}<sub>0≤i≤d</sub>) and association scheme of class d on X. The non-neg...constant whenever （x, y）∈Rk. This constant is denoted by p<sub>ij</sub><sup>k</sup>. Then we call X=(X,{Ri}<sub>0≤i≤d</sub>) and association scheme of class d on X. The non-negative integers p<sub>ij</sub><sup>k</sup> are called the intersection numbers of X.展开更多
Association schemes have close connections with coding, design and finite group theory, etc. In 1965, Wan Zhe-xian first discussed the association schemes based on the n×n Hermitian matrices over finite fields, a...Association schemes have close connections with coding, design and finite group theory, etc. In 1965, Wan Zhe-xian first discussed the association schemes based on the n×n Hermitian matrices over finite fields, and calculated their parameters when n=2. Later,Wang Yang-xian gave a recurrence calculation formula of展开更多
For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij<...For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij</sub>},（1）B=(b<sub>ij</sub>)<sub>n×n</sub>=B<sup>T</sup>,C=(c<sub>ij</sub>)<sub>n×n</sub>=C<sup>T</sup>∈R<sup>n×n</sup>,Bialas has studied the necessary and sufficient condi-tion of asymptotic stabilty of G[B,C].According to refs[2-6],the following result,the asympotic stability of G[B,C],can be obtained if that of its subsetH[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>∈G[B,C],a<sub>ij</sub>=b<sub>ij</sub> or c<sub>ij</sub>}. （2）展开更多
Let X_n be the set of n×n symmetric matrices over a finite field F_q,where q is a power of an odd prime.For S_1,S_2 ∈ X_n,we define (S_1,S_2)∈ R_0 iff S_1=S_2;(S_1,S_2)∈R_(r,ε)iff S_1-S_2 is congruent to wher...Let X_n be the set of n×n symmetric matrices over a finite field F_q,where q is a power of an odd prime.For S_1,S_2 ∈ X_n,we define (S_1,S_2)∈ R_0 iff S_1=S_2;(S_1,S_2)∈R_(r,ε)iff S_1-S_2 is congruent to where?=1 or z,z being afixed non-square element of F_q.Then X_n=(X_n,{R_0,R_(r,ε)|1≤r≤n,?=1 or z}) is a non-symmetric association scheme of class 2n on X_n.The parameters of X_n have been computed.And we also prove that X_n is commutative.展开更多
文摘In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign pattern matrix (or sign pattern).For a re-al matrix B,by sgn (B) we mean the sign pattern matrix in which each positive (respec-tively,negative,zero) entry of B is replaced by+(respectively,-,0).If A is an
文摘In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied entrywise.
文摘Main resultsTheorem 1 Let A be symmetric positive semidefinite.Let (?) be a diagonally compen-sated reduced matrix of A and Let (?)=σI+(?)(σ】0) be a modiffication(Stieltjes) matrixof (?).Let the splitting (?)=M-(?) be regular and M=F-G be weak regular,where M andF are symmetric positive definite matrices.Then the resulting two-stage method corre-sponding to the diagonally compensated reduced splitting A=M-N and inner splitting M=F-G is convergent for any number μ≥1 of inner iterations.Furthermore,the
文摘In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deflation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saunders’ MINRES method for iterative solution of symmetric linear systems, and describe important implementation details. We establish a relationship between the block Lanczos algorithm and block MINRES algorithm, and compare the numerical performance of the Lanczos algorithm and MINRES method for symmetric linear systems applied to a sequence of right hand sides with that of the block Lanczos algorithm and block MINRES algorithm for multiple linear systems simultaneously.[WT5,5”HZ]
基金the National Natural Science Foundation of China under Grants 61673012 and 11971240,respectively。
文摘In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.
文摘constant whenever （x, y）∈Rk. This constant is denoted by p<sub>ij</sub><sup>k</sup>. Then we call X=(X,{Ri}<sub>0≤i≤d</sub>) and association scheme of class d on X. The non-negative integers p<sub>ij</sub><sup>k</sup> are called the intersection numbers of X.
文摘Association schemes have close connections with coding, design and finite group theory, etc. In 1965, Wan Zhe-xian first discussed the association schemes based on the n×n Hermitian matrices over finite fields, and calculated their parameters when n=2. Later,Wang Yang-xian gave a recurrence calculation formula of
文摘For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij</sub>},（1）B=(b<sub>ij</sub>)<sub>n×n</sub>=B<sup>T</sup>,C=(c<sub>ij</sub>)<sub>n×n</sub>=C<sup>T</sup>∈R<sup>n×n</sup>,Bialas has studied the necessary and sufficient condi-tion of asymptotic stabilty of G[B,C].According to refs[2-6],the following result,the asympotic stability of G[B,C],can be obtained if that of its subsetH[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>∈G[B,C],a<sub>ij</sub>=b<sub>ij</sub> or c<sub>ij</sub>}. （2）
文摘Let X_n be the set of n×n symmetric matrices over a finite field F_q,where q is a power of an odd prime.For S_1,S_2 ∈ X_n,we define (S_1,S_2)∈ R_0 iff S_1=S_2;(S_1,S_2)∈R_(r,ε)iff S_1-S_2 is congruent to where?=1 or z,z being afixed non-square element of F_q.Then X_n=(X_n,{R_0,R_(r,ε)|1≤r≤n,?=1 or z}) is a non-symmetric association scheme of class 2n on X_n.The parameters of X_n have been computed.And we also prove that X_n is commutative.
