Cloud computing provides the capability to con-nect resource-constrained clients with a centralized and shared pool of resources,such as computational power and storage on demand.Large matrix determinant computation i...Cloud computing provides the capability to con-nect resource-constrained clients with a centralized and shared pool of resources,such as computational power and storage on demand.Large matrix determinant computation is almost ubiquitous in computer science and requires large-scale data computation.Currently,techniques for securely outsourcing matrix determinant computations to untrusted servers are of utmost importance,and they have practical value as well as theoretical significance for the scientific community.In this study,we propose a secure outsourcing method for large matrix determinant computation.We em-ploy some transformations for privacy protection based on the original matrix,including permutation and mix-row/mix-column operations,before sending the target matrix to the cloud.The results returned from the cloud need to be de-clypled anul verified U ubtainl te cullett delinall.Il1 comparison with previously proposed algorithms,our new al-gorithm achieves a higher security level with greater cloud ef-ficiency.The experimental results demonstrate the efficiency and effectiveness of our algorithm.展开更多
Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded...Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit. Nested form is neither canonical nor amenable to symbolic manipulation. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. This algorithm, called totally coded method (TCM), consists of representing the symbolic determinant of a circuit matrix by code series and performing symbolic analysis by code manipulation. We describe an efficient code-ordering heuristic and prove that it is optimum for ladder-structured circuits. For practical analog circuits, TCM not only covers all advantages of the algorithm via determinant decision diagrams (DDD) but is more simple and efficient than DDD method.展开更多
By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition,...By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition, 1999, 19（3）： 598-600）, HE Gan-tong （J. Math. Res. Exposition, 2002, 22（1）： 79-82） and YUAN Hui-ping （J. Math. Res. Exposition, 2001, 21（3）： 464-468） are wrong. In this note, we point out that the counterexample is wrong. Further discussion on these assertions and some related results are also given.展开更多
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the g...This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61502269)National Key Research and Development Program of China(2017YFA0303903)Zhejiang Province Key R&D Project(2017C01062).
文摘Cloud computing provides the capability to con-nect resource-constrained clients with a centralized and shared pool of resources,such as computational power and storage on demand.Large matrix determinant computation is almost ubiquitous in computer science and requires large-scale data computation.Currently,techniques for securely outsourcing matrix determinant computations to untrusted servers are of utmost importance,and they have practical value as well as theoretical significance for the scientific community.In this study,we propose a secure outsourcing method for large matrix determinant computation.We em-ploy some transformations for privacy protection based on the original matrix,including permutation and mix-row/mix-column operations,before sending the target matrix to the cloud.The results returned from the cloud need to be de-clypled anul verified U ubtainl te cullett delinall.Il1 comparison with previously proposed algorithms,our new al-gorithm achieves a higher security level with greater cloud ef-ficiency.The experimental results demonstrate the efficiency and effectiveness of our algorithm.
文摘Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit. Nested form is neither canonical nor amenable to symbolic manipulation. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. This algorithm, called totally coded method (TCM), consists of representing the symbolic determinant of a circuit matrix by code series and performing symbolic analysis by code manipulation. We describe an efficient code-ordering heuristic and prove that it is optimum for ladder-structured circuits. For practical analog circuits, TCM not only covers all advantages of the algorithm via determinant decision diagrams (DDD) but is more simple and efficient than DDD method.
基金Supported by the Natural Science Foundation of Science and Technology Office of Guizhou Province (Grant No. J[2006]2002)
文摘By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition, 1999, 19（3）： 598-600）, HE Gan-tong （J. Math. Res. Exposition, 2002, 22（1）： 79-82） and YUAN Hui-ping （J. Math. Res. Exposition, 2001, 21（3）： 464-468） are wrong. In this note, we point out that the counterexample is wrong. Further discussion on these assertions and some related results are also given.
基金This research is supported by the Natural Science Foundation of the Educational Committee of Jiang Su Province.
文摘This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.
