A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directl...A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.展开更多
Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elim...Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting （GESP） method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.展开更多
Judice and Pires developed in recent years principal pivoting methods for the solving of the so called box linear complementarity problems (BLCPs) where the constraint matrices are restrictedly supposed to be of P ...Judice and Pires developed in recent years principal pivoting methods for the solving of the so called box linear complementarity problems (BLCPs) where the constraint matrices are restrictedly supposed to be of P matrices. This paper aims at presenting a new principal pivoting scheme for BLCPs where the constraint matrices are loosely supposed to be row sufficient.This scheme can be applied to the solving of convex quadratic programs subject to linear constraints and arbitrary upper and lower bound constraints on variables.展开更多
To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventiona...To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventional condition that some function value increases monotonically, but also the condition that all feasible variables remain feasible after basis change in Phase-1. That is, taking a purely combinatorial approach to achieving feasibility. This enables us to get rid of ratio test in pivoting, reducing computational cost per iteration to a large extent. Numerical results on a group of problems are encouraging.展开更多
Neural machine translation(NMT)has been widely applied to high-resource language pairs,but its dependence on large-scale data results in poor performance in low-resource scenarios.In this paper,we propose a transfer-l...Neural machine translation(NMT)has been widely applied to high-resource language pairs,but its dependence on large-scale data results in poor performance in low-resource scenarios.In this paper,we propose a transfer-learning-based approach called shared space transfer for zero-resource NMT.Our method leverages a pivot pre-trained language model(PLM)to create a shared representation space,which is used in both auxiliary source→pivot(Ms2p)and(Mp2t)translation models.Specifically,we exploit pivot PLM to initialize the Ms2p decoder pivot→targetand Mp2t encoder,while adopting a freezing strategy during the training process.We further propose a feature converter to mitigate representation space deviations by converting the features from the source encoder into the shared representation space.The converter is trained using the synthetic parallel corpus.The final Ms2t model source→targetcombines the Ms2p encoder,feature converter,and Mp2t decoder.We conduct simulation experiments using English as the pivot language for and translations.We finally test our method German→French,German→Czech,Turkish→Hindion a real zero-resource language pair,with Chinese as the pivot language.Experiment results Mongolian→Vietnameseshow that our method achieves high translation quality,with better Translation Error Rate(TER)and BLEU scores compared with other pivot-based methods.The step-wise pre-training with our feature converter outperforms baseline models in terms of COMET scores.展开更多
This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-eliminat...This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.展开更多
Despite it is often available in practice, information of optimal value of linear programming problems is ignored by conventional simplex algorithms. To speed up solution process, we propose in this paper some vari...Despite it is often available in practice, information of optimal value of linear programming problems is ignored by conventional simplex algorithms. To speed up solution process, we propose in this paper some variants of the bisection algorithm, explo展开更多
This study investigates the redesign of a structural system with the matrix modification. The inertia congruence transformation is adopted to find the latent roots of a dynamic stiffness matrix, and a method for deter...This study investigates the redesign of a structural system with the matrix modification. The inertia congruence transformation is adopted to find the latent roots of a dynamic stiffness matrix, and a method for determining its eigenvalue is proposed. The characteristics of the latent vector for a known latent root and a method for computing it are studied. The mode shapes of the redesigned structure must be differently handled based on whether the structure exhibits persistent or non-persistent natural frequencies.展开更多
This paper deals with the existince of the solulionlor linear complementaryproblern. The uniqueness theorem of lhe solution for linear compiementary. problem isproved. Two evaniples are given. They show that “M is po...This paper deals with the existince of the solulionlor linear complementaryproblern. The uniqueness theorem of lhe solution for linear compiementary. problem isproved. Two evaniples are given. They show that “M is positive .sermidefinite”neither sufficient nor necessary codition .for te, existence to the solution of linearcomplementary. problem.展开更多
基金The National Natural Science Foundation of China (No.61374194)
文摘A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.
基金supported by China State Key Science and Technology Project on Marine Carbonate Reservoir Characterization (No. 2008ZX05004-006)
文摘Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting （GESP） method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.
文摘Judice and Pires developed in recent years principal pivoting methods for the solving of the so called box linear complementarity problems (BLCPs) where the constraint matrices are restrictedly supposed to be of P matrices. This paper aims at presenting a new principal pivoting scheme for BLCPs where the constraint matrices are loosely supposed to be row sufficient.This scheme can be applied to the solving of convex quadratic programs subject to linear constraints and arbitrary upper and lower bound constraints on variables.
文摘To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventional condition that some function value increases monotonically, but also the condition that all feasible variables remain feasible after basis change in Phase-1. That is, taking a purely combinatorial approach to achieving feasibility. This enables us to get rid of ratio test in pivoting, reducing computational cost per iteration to a large extent. Numerical results on a group of problems are encouraging.
基金funded by the National Natural Science Foundation of China(Grant number:Nos.62172341 and 12204386)Sichuan Natural Science Foundation(Grant number:No.2024NSFSC1375)+1 种基金Youth Foundation of Inner Mongolia Natural Science Foundation(Grant number:No.2024QN06017)Basic Scientific Research Business Fee Project for Universities in Inner Mongolia(Grant number:No.0406082215).
文摘Neural machine translation(NMT)has been widely applied to high-resource language pairs,but its dependence on large-scale data results in poor performance in low-resource scenarios.In this paper,we propose a transfer-learning-based approach called shared space transfer for zero-resource NMT.Our method leverages a pivot pre-trained language model(PLM)to create a shared representation space,which is used in both auxiliary source→pivot(Ms2p)and(Mp2t)translation models.Specifically,we exploit pivot PLM to initialize the Ms2p decoder pivot→targetand Mp2t encoder,while adopting a freezing strategy during the training process.We further propose a feature converter to mitigate representation space deviations by converting the features from the source encoder into the shared representation space.The converter is trained using the synthetic parallel corpus.The final Ms2t model source→targetcombines the Ms2p encoder,feature converter,and Mp2t decoder.We conduct simulation experiments using English as the pivot language for and translations.We finally test our method German→French,German→Czech,Turkish→Hindion a real zero-resource language pair,with Chinese as the pivot language.Experiment results Mongolian→Vietnameseshow that our method achieves high translation quality,with better Translation Error Rate(TER)and BLEU scores compared with other pivot-based methods.The step-wise pre-training with our feature converter outperforms baseline models in terms of COMET scores.
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.
文摘Despite it is often available in practice, information of optimal value of linear programming problems is ignored by conventional simplex algorithms. To speed up solution process, we propose in this paper some variants of the bisection algorithm, explo
文摘This study investigates the redesign of a structural system with the matrix modification. The inertia congruence transformation is adopted to find the latent roots of a dynamic stiffness matrix, and a method for determining its eigenvalue is proposed. The characteristics of the latent vector for a known latent root and a method for computing it are studied. The mode shapes of the redesigned structure must be differently handled based on whether the structure exhibits persistent or non-persistent natural frequencies.
文摘This paper deals with the existince of the solulionlor linear complementaryproblern. The uniqueness theorem of lhe solution for linear compiementary. problem isproved. Two evaniples are given. They show that “M is positive .sermidefinite”neither sufficient nor necessary codition .for te, existence to the solution of linearcomplementary. problem.
