Finding the nearest volume-preserving matrix for a given matrix is studied. Amatrix equation is first obtained, which is a necessary condition for the solution to the problem.Then the equation is solved by the singula...Finding the nearest volume-preserving matrix for a given matrix is studied. Amatrix equation is first obtained, which is a necessary condition for the solution to the problem.Then the equation is solved by the singular value decomposition method. Some additional results arealso provided to further characterize the solution. Using these results, a numerical algorithm isintroduced and a numerical test is given to illustrate the effectiveness of the algorithm.展开更多
The inverse problem to determine the vibrating velocity from known exteriorfield measurement pressure, involves the solution of a discrete ill-posed problem. To facilitate thecomputation of a meaningful approximate so...The inverse problem to determine the vibrating velocity from known exteriorfield measurement pressure, involves the solution of a discrete ill-posed problem. To facilitate thecomputation of a meaningful approximate solution possible, the indirect boundary element method(IBEM) code for investigating vibration velocity reconstruction and Tikhonov regularization methodby means of singular value decomposition (SVD) are used. The amount of regularization is determinedby a regularization parameter. Its optimal value is given by the L-curve approach. Numerical resultsindicate the reconstructed normal surface velocity is a good approximation to the real source.展开更多
To sample non-bandlimited impulse signals, an extremely high-sampling rate analog-todigital converters （ADC） is required. Such an ADC is very difficult to be implemented with present semiconductor technology. In thi...To sample non-bandlimited impulse signals, an extremely high-sampling rate analog-todigital converters （ADC） is required. Such an ADC is very difficult to be implemented with present semiconductor technology. In this paper, a novel sampling and reconstruction method for impulse signals is proposed. The required sampling rate of the proposed method is close to the signal innovation rate, which is much lower than the Nyquist rate in conventional Shannon sampling theory. Analysis and simulation results show that the proposed method can achieve very good reconstruction performance in the presence of noise.展开更多
文摘Finding the nearest volume-preserving matrix for a given matrix is studied. Amatrix equation is first obtained, which is a necessary condition for the solution to the problem.Then the equation is solved by the singular value decomposition method. Some additional results arealso provided to further characterize the solution. Using these results, a numerical algorithm isintroduced and a numerical test is given to illustrate the effectiveness of the algorithm.
文摘The inverse problem to determine the vibrating velocity from known exteriorfield measurement pressure, involves the solution of a discrete ill-posed problem. To facilitate thecomputation of a meaningful approximate solution possible, the indirect boundary element method(IBEM) code for investigating vibration velocity reconstruction and Tikhonov regularization methodby means of singular value decomposition (SVD) are used. The amount of regularization is determinedby a regularization parameter. Its optimal value is given by the L-curve approach. Numerical resultsindicate the reconstructed normal surface velocity is a good approximation to the real source.
基金supported by the National Natural Science Foundation of Chinaunder Grant No 60496313
文摘To sample non-bandlimited impulse signals, an extremely high-sampling rate analog-todigital converters （ADC） is required. Such an ADC is very difficult to be implemented with present semiconductor technology. In this paper, a novel sampling and reconstruction method for impulse signals is proposed. The required sampling rate of the proposed method is close to the signal innovation rate, which is much lower than the Nyquist rate in conventional Shannon sampling theory. Analysis and simulation results show that the proposed method can achieve very good reconstruction performance in the presence of noise.
