Let J. be an n × n Jacobi matrix and Al λ1 ,..',λ2n distinct real numbers. The following problem is well known. Under what condition does there exist a 2n × 2n Jacobi matrix J. such that J,. has eige...Let J. be an n × n Jacobi matrix and Al λ1 ,..',λ2n distinct real numbers. The following problem is well known. Under what condition does there exist a 2n × 2n Jacobi matrix J. such that J,. has eigenvalues λ1, ..λ2n A. and its leading n × n principal submatrix is exactly Jn In this paper a condition for the solubility of the problem is given. The dependence of J2n on the given data is shown to be continuous.展开更多
The Wielandt-Hoffman theorem of the real symmetric matrix is extended into a plural matrix. On the basis of it, a similar theory about the trace of a matrix for the arithmetic mean, geometric mean inequality, Holder i...The Wielandt-Hoffman theorem of the real symmetric matrix is extended into a plural matrix. On the basis of it, a similar theory about the trace of a matrix for the arithmetic mean, geometric mean inequality, Holder inequality and Minkowski inequality is proved.展开更多
对于一类非线性信号的去噪问题,该文提出一种基于奇异值分解(Singular Value Decomposition,SVD)的有效迭代方法。对现有奇异值差分谱方法在两类不同非线性信号上的去噪效果进行了对比,指出在信号不具有明显特征频率、非周期性变化时这...对于一类非线性信号的去噪问题,该文提出一种基于奇异值分解(Singular Value Decomposition,SVD)的有效迭代方法。对现有奇异值差分谱方法在两类不同非线性信号上的去噪效果进行了对比,指出在信号不具有明显特征频率、非周期性变化时这一方法并不适用,并分析了现象产生的原因;然后针对该类信号的特点重新定义了Hankel矩阵结构,给出有效奇异值的确定方式,并通过SVD多次迭代过程实现对该类信号的有效去噪。对实际飞行数据去噪的实验结果表明,该方法对提出的一类信号对象不仅去噪效果良好,而且可提高运算效率。展开更多
文摘Let J. be an n × n Jacobi matrix and Al λ1 ,..',λ2n distinct real numbers. The following problem is well known. Under what condition does there exist a 2n × 2n Jacobi matrix J. such that J,. has eigenvalues λ1, ..λ2n A. and its leading n × n principal submatrix is exactly Jn In this paper a condition for the solubility of the problem is given. The dependence of J2n on the given data is shown to be continuous.
文摘The Wielandt-Hoffman theorem of the real symmetric matrix is extended into a plural matrix. On the basis of it, a similar theory about the trace of a matrix for the arithmetic mean, geometric mean inequality, Holder inequality and Minkowski inequality is proved.
文摘对于一类非线性信号的去噪问题,该文提出一种基于奇异值分解(Singular Value Decomposition,SVD)的有效迭代方法。对现有奇异值差分谱方法在两类不同非线性信号上的去噪效果进行了对比,指出在信号不具有明显特征频率、非周期性变化时这一方法并不适用,并分析了现象产生的原因;然后针对该类信号的特点重新定义了Hankel矩阵结构,给出有效奇异值的确定方式,并通过SVD多次迭代过程实现对该类信号的有效去噪。对实际飞行数据去噪的实验结果表明,该方法对提出的一类信号对象不仅去噪效果良好,而且可提高运算效率。
