We present componentwise condition numbers for the problems of MoorePenrose generalized matrix inversion and linear least squares. Also, the condition numbers for these condition numbers are given.
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learnin...Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learning.A Conditional Variational Auto Encoder(CVAE)and an integrated generative network CVAE-GAN that combines the CVAE with the Wasserstein Generative Adversarial Networks(WGAN),are conducted as generative models.They are used to generate target wall Mach distributions for the inverse design that matches specified features,such as locations of suction peak,shock and aft loading.Qualitative and quantitative results show that both adopted generative models can generate diverse and realistic wall Mach number distributions satisfying the given features.The CVAE-GAN model outperforms the CVAE model and achieves better reconstruction accuracies for all the samples in the dataset.Furthermore,a deep neural network for nonlinear mapping is adopted to obtain the airfoil shape corresponding to the target wall Mach number distribution.The performances of the designed deep neural network are fully demonstrated and a smoothness measurement is proposed to quantify small oscillations in the airfoil surface,proving the authenticity and accuracy of the generated airfoil shapes.展开更多
The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions fo...The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.展开更多
Elastography is a non-invasive medical imaging technique to map the spatial variation of elastic properties of soft tissues.The quality of reconstruction results in elastography is highly sensitive to the noise induce...Elastography is a non-invasive medical imaging technique to map the spatial variation of elastic properties of soft tissues.The quality of reconstruction results in elastography is highly sensitive to the noise induced by imaging measurements and processing.To address this issue,we propose a deep learning(DL)model based on conditional Generative Adversarial Networks(cGANs)to improve the quality of nonhomogeneous shear modulus reconstruction.To train this model,we generated a synthetic displacement field with finite element simulation under known nonhomogeneous shear modulus distribution.Both the simulated and experimental displacement fields are used to validate the proposed method.The reconstructed results demonstrate that the DL model with synthetic training data is able to improve the quality of the reconstruction compared with the well-established optimization method.Moreover,we emphasize that our DL model is only trained on synthetic data.This might provide a way to alleviate the challenge of obtaining clinical or experimental data in elastography.Overall,this work addresses several fatal issues in applying the DL technique into elastography,and the proposed method has shown great potential in improving the accuracy of the disease diagnosis in clinical medicine.展开更多
The class of symmetric definitely positive matrices is extremely important in the matrix theory. At present, positive definiteness of a symmetric matrix can be shown by determining the signs of its all ordered princip...The class of symmetric definitely positive matrices is extremely important in the matrix theory. At present, positive definiteness of a symmetric matrix can be shown by determining the signs of its all ordered principal minors or the signs展开更多
基金the NSF of China under grant 10471027 and Shanghai Education Commission.
文摘We present componentwise condition numbers for the problems of MoorePenrose generalized matrix inversion and linear least squares. Also, the condition numbers for these condition numbers are given.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
文摘We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
基金co-supported by the National Key Project of China(No.GJXM92579)the National Natural Science Foundation of China(Nos.92052203,61903178 and61906081)。
文摘Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learning.A Conditional Variational Auto Encoder(CVAE)and an integrated generative network CVAE-GAN that combines the CVAE with the Wasserstein Generative Adversarial Networks(WGAN),are conducted as generative models.They are used to generate target wall Mach distributions for the inverse design that matches specified features,such as locations of suction peak,shock and aft loading.Qualitative and quantitative results show that both adopted generative models can generate diverse and realistic wall Mach number distributions satisfying the given features.The CVAE-GAN model outperforms the CVAE model and achieves better reconstruction accuracies for all the samples in the dataset.Furthermore,a deep neural network for nonlinear mapping is adopted to obtain the airfoil shape corresponding to the target wall Mach number distribution.The performances of the designed deep neural network are fully demonstrated and a smoothness measurement is proposed to quantify small oscillations in the airfoil surface,proving the authenticity and accuracy of the generated airfoil shapes.
文摘The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.
基金National Natural Science Foundation of China (12002075)National Key Research and Development Project (2021YFB3300601)Natural Science Foundation of Liaoning Province in China (2021-MS-128).
文摘Elastography is a non-invasive medical imaging technique to map the spatial variation of elastic properties of soft tissues.The quality of reconstruction results in elastography is highly sensitive to the noise induced by imaging measurements and processing.To address this issue,we propose a deep learning(DL)model based on conditional Generative Adversarial Networks(cGANs)to improve the quality of nonhomogeneous shear modulus reconstruction.To train this model,we generated a synthetic displacement field with finite element simulation under known nonhomogeneous shear modulus distribution.Both the simulated and experimental displacement fields are used to validate the proposed method.The reconstructed results demonstrate that the DL model with synthetic training data is able to improve the quality of the reconstruction compared with the well-established optimization method.Moreover,we emphasize that our DL model is only trained on synthetic data.This might provide a way to alleviate the challenge of obtaining clinical or experimental data in elastography.Overall,this work addresses several fatal issues in applying the DL technique into elastography,and the proposed method has shown great potential in improving the accuracy of the disease diagnosis in clinical medicine.
基金Project supported by the National Natural Science Foundation of China.
文摘The class of symmetric definitely positive matrices is extremely important in the matrix theory. At present, positive definiteness of a symmetric matrix can be shown by determining the signs of its all ordered principal minors or the signs
