In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a...In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.展开更多
Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M m...Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.展开更多
A matrix whose entries are +,-, and 0 is called a sign pattern matrix. For a sign pattern matrix A , if A 3=A , then A is said to be sign tripotent. In this paper, the characterization of the n by n(n...A matrix whose entries are +,-, and 0 is called a sign pattern matrix. For a sign pattern matrix A , if A 3=A , then A is said to be sign tripotent. In this paper, the characterization of the n by n(n≥2) sign pattern matrices A which are sign tripotent has been given out. Furthermore, the necessary and sufficient condition of A 3=A but A 2≠A is obtained, too.展开更多
针对目标检测算法在交通标志检测中存在的不足,文中提出了一种融合感受野增强模块和注意力机制的交通标志检测算法。该算法在YOLOv5(You Only Look Once version 5)算法的基础上改进,选用感受野模块(Receptive Field Block,RFB)替换原...针对目标检测算法在交通标志检测中存在的不足,文中提出了一种融合感受野增强模块和注意力机制的交通标志检测算法。该算法在YOLOv5(You Only Look Once version 5)算法的基础上改进,选用感受野模块(Receptive Field Block,RFB)替换原骨干网络中的空间金字塔池化(Spatial Pyramid Pooling,SPP)模块,在特征融合网络中嵌入高效通道注意模块(Efficient Channel Attention Module,ECAM)和卷积块注意模块(Convolutional Block Attention Module,CBAM),选用矩阵非极大值抑制(Matrix Non-Maximum Suppression,Matrix NMS)筛选候选框以提升算法的检测精度和检测速度。实验结果表明,在模型参数量与原网络相比未变化的前提下,该算法的均值平均精度达到了82.31%,与原算法相比提升了8.59%,检测速度达到了51.89 frame·s^(-1),且该算法在各个测试场景中未出现错检漏检现象,证明其泛化能力优于原算法,可以实时检测交通标志。展开更多
A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generall...A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative tri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.展开更多
Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review...Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review, modify and combine various techniques of numerical linear algebra and rational algebraic computations (with no error) to achieve our main goal of decreasing the bit-precision for computing detA or its sign and enable us to obtain the solution with few arithmetic operations. In particular, we improved the precision bits of the p-adic lifting algorithm (H = 2h for a natural number h), which may exceed the computer precision β (see Section 5.2), to at most bits (see Section 6). The computational cost of the p-adic lifting can be performed in O(hn4). We reduced this cost to O(n3) by employing the faster p-adic lifting technique (see Section 5.3).展开更多
文摘In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.
文摘Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.
基金Project supported by the National Natural Science Foundation of China(1 9971 0 86)
文摘A matrix whose entries are +,-, and 0 is called a sign pattern matrix. For a sign pattern matrix A , if A 3=A , then A is said to be sign tripotent. In this paper, the characterization of the n by n(n≥2) sign pattern matrices A which are sign tripotent has been given out. Furthermore, the necessary and sufficient condition of A 3=A but A 2≠A is obtained, too.
文摘针对目标检测算法在交通标志检测中存在的不足,文中提出了一种融合感受野增强模块和注意力机制的交通标志检测算法。该算法在YOLOv5(You Only Look Once version 5)算法的基础上改进,选用感受野模块(Receptive Field Block,RFB)替换原骨干网络中的空间金字塔池化(Spatial Pyramid Pooling,SPP)模块,在特征融合网络中嵌入高效通道注意模块(Efficient Channel Attention Module,ECAM)和卷积块注意模块(Convolutional Block Attention Module,CBAM),选用矩阵非极大值抑制(Matrix Non-Maximum Suppression,Matrix NMS)筛选候选框以提升算法的检测精度和检测速度。实验结果表明,在模型参数量与原网络相比未变化的前提下,该算法的均值平均精度达到了82.31%,与原算法相比提升了8.59%,检测速度达到了51.89 frame·s^(-1),且该算法在各个测试场景中未出现错检漏检现象,证明其泛化能力优于原算法,可以实时检测交通标志。
文摘A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative tri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.
文摘Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review, modify and combine various techniques of numerical linear algebra and rational algebraic computations (with no error) to achieve our main goal of decreasing the bit-precision for computing detA or its sign and enable us to obtain the solution with few arithmetic operations. In particular, we improved the precision bits of the p-adic lifting algorithm (H = 2h for a natural number h), which may exceed the computer precision β (see Section 5.2), to at most bits (see Section 6). The computational cost of the p-adic lifting can be performed in O(hn4). We reduced this cost to O(n3) by employing the faster p-adic lifting technique (see Section 5.3).
