A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. Th...A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.展开更多
The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covarian...The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.展开更多
The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise w...The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.展开更多
Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, ...Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=[0 A C B]is given under the condition of EBF - 0, where E - I - CCT and F - I -AfA. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M =[0 a In b]due to Pedro Patricio. As for applications, some examples are given to illustrate the obtained results.展开更多
A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. T...A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.展开更多
An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new al...An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.展开更多
The plasma sheath can induce radar signal modulation,causing not only ineffective target detection,but also defocusing in inverse synthetic aperture radar(ISAR)imaging.In this paper,through establishing radar echo mod...The plasma sheath can induce radar signal modulation,causing not only ineffective target detection,but also defocusing in inverse synthetic aperture radar(ISAR)imaging.In this paper,through establishing radar echo models of the reentry object enveloped with time-varying plasma sheath,we simulated the defocusing of ISAR images in typical environment.Simulation results suggested that the ISAR defocusing is caused by false scatterings,upon which the false scatterings’formation mechanism and distribution property are analyzed and studied.The range of false scattering correlates with the electron density fluctuation frequency.The combined value of the electron density fluctuation and the pulse repetition frequency jointly determines the Doppler of false scattering.Two measurement metrics including peak signal-to-noise ratio and structural similarity are used to evaluate the influence of ISAR imaging.展开更多
This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form,...This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form, then exporting flat quaternions base in two matrix form. It establishes serial 6R manipulator kinematic equations in the form of quaternion matrix. Then five variables are eliminated through linear elimination and application of lexicographic Groebner base. Thus, upper bound of the degree of the equation is determined, which is 16. In this way, a 16-degree equation with single variable is obtained without any extraneous root. This is the first time that quaternion matrix modeling has been used in 6R robot inverse kinematics analysis.展开更多
A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical...A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.展开更多
Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. Th...Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. The best approximate solution by the above solution set is given. Thus the open problem in [1] is solved.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
When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to ...When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of is sought in the form if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations.展开更多
In this article, the expression for the Drazin inverse of a modified matrix is considered and some interesting results are established. This contributes to certain recent results obtained by Y.Wei [9].
In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fra...In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.展开更多
In this paper, we present a method how to get the expression for the group inverse of 2×2 block matrix and get the explicit expressions of the block matrix (A C B D) under some conditions.
The Γα-group inverse and the Γα-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γα-sharp ordering are given. The relations between the Γα-sharp ordering and the Γα-m...The Γα-group inverse and the Γα-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γα-sharp ordering are given. The relations between the Γα-sharp ordering and the Γα-minus ordering are discussed.展开更多
Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub&...Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is展开更多
Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in si...Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in sick children is very challenging for clinicians who frequently rely on indices such as long capillary refill times, tachycardia, central venous pressure and decreased urine volume as guides. Here, we present the UHAS-MIDA, an open-source software tool that calculates the red blood cell (RBC) concentration and blood volume during malaria in children determined using a stable isotope of chromium (<sup>53</sup>Cr as the label) by gas chromatography-mass spectrometry in selective ion monitoring (GC/MS-SIM) analysis. A key component involves the determination of the compositions of the most abundant naturally occurring isotopes of Cr (<sup>50</sup>Cr, <sup>52</sup>Cr, <sup>53</sup>Cr), and converting the proportions into a 3 × 3 matrix. To estimate unknown proportions of chromium isotopic mixtures from the measured abundances of three ions, an inverse matrix was calculated. The inverse together with several inputs is then used to calculate the corrected MS ion abundances. Thus, we constructed the software tool UHAS- MIDA using HTML, CSS/Bootstrap, JavaScript, and PHP scripting languages. The tool enables the user to efficiently determine RBC concentration and fluid volume. The source code, binary packages and associated materials for UHAS-MIDA are freely available at https://github.com/bentil078/Abaye-et-al_UHASmida展开更多
This study focuses on estimating O-D （origin-destination） trip demand from link traffic flows. Equality relationship among link traffic flow, path flow, and O-D trip matrices are used to establish a linear equation ...This study focuses on estimating O-D （origin-destination） trip demand from link traffic flows. Equality relationship among link traffic flow, path flow, and O-D trip matrices are used to establish a linear equation system. Solution characteristics are analyzed based on the relationship between the rank of the link/path incidence matrix and column variables. And under the solution framework of conditional inverse matrices, a column exchange method and a path flow proportion method have been developed. Network testing results verify that the proposed methods yield good results.展开更多
文摘A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.
文摘The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.
文摘The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.
基金The National Natural Science Foundation of China(No.11371089)the Natural Science Foundation of Jiangsu Province(No.BK20141327)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Natural Science Foundation of Jiangsu Higher Education Institutions of China(No.15KJB110021)
文摘Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=[0 A C B]is given under the condition of EBF - 0, where E - I - CCT and F - I -AfA. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M =[0 a In b]due to Pedro Patricio. As for applications, some examples are given to illustrate the obtained results.
文摘A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.
文摘An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.
基金supported in part by National Natural Science Foundation of China(Nos.61971330,61701381,and 61627901)in part by the Natural Science Basic Research Plan in Shaanxi Province of China(No.2019JM-177)in part by the Chinese Postdoctoral Science Foundation。
文摘The plasma sheath can induce radar signal modulation,causing not only ineffective target detection,but also defocusing in inverse synthetic aperture radar(ISAR)imaging.In this paper,through establishing radar echo models of the reentry object enveloped with time-varying plasma sheath,we simulated the defocusing of ISAR images in typical environment.Simulation results suggested that the ISAR defocusing is caused by false scatterings,upon which the false scatterings’formation mechanism and distribution property are analyzed and studied.The range of false scattering correlates with the electron density fluctuation frequency.The combined value of the electron density fluctuation and the pulse repetition frequency jointly determines the Doppler of false scattering.Two measurement metrics including peak signal-to-noise ratio and structural similarity are used to evaluate the influence of ISAR imaging.
文摘This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form, then exporting flat quaternions base in two matrix form. It establishes serial 6R manipulator kinematic equations in the form of quaternion matrix. Then five variables are eliminated through linear elimination and application of lexicographic Groebner base. Thus, upper bound of the degree of the equation is determined, which is 16. In this way, a 16-degree equation with single variable is obtained without any extraneous root. This is the first time that quaternion matrix modeling has been used in 6R robot inverse kinematics analysis.
文摘A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.
文摘Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. The best approximate solution by the above solution set is given. Thus the open problem in [1] is solved.
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.
文摘When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of is sought in the form if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations.
基金Supported by Grant No. 174007 of the Ministry of Science,Technology and Development,Republic of Serbia
文摘In this article, the expression for the Drazin inverse of a modified matrix is considered and some interesting results are established. This contributes to certain recent results obtained by Y.Wei [9].
文摘In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.
基金Supported by the Fund for Postdoctoral of China(2015M581688)Supported by the National Natural Science Foundation of China(11371089)+2 种基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education(20120092110020)Supported by the Natural Science Foundation of Jiangsu Province(BK20141327)Supported by the Foundation of Xuzhou Institute of Technology(XKY2014207)
文摘In this paper, we present a method how to get the expression for the group inverse of 2×2 block matrix and get the explicit expressions of the block matrix (A C B D) under some conditions.
基金the National Sciennce Foundation of Zhejiang Province(Y604089)
文摘The Γα-group inverse and the Γα-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γα-sharp ordering are given. The relations between the Γα-sharp ordering and the Γα-minus ordering are discussed.
基金The works is supported by the National Natural Science Foundation of China(19871054)
文摘Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is
文摘Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in sick children is very challenging for clinicians who frequently rely on indices such as long capillary refill times, tachycardia, central venous pressure and decreased urine volume as guides. Here, we present the UHAS-MIDA, an open-source software tool that calculates the red blood cell (RBC) concentration and blood volume during malaria in children determined using a stable isotope of chromium (<sup>53</sup>Cr as the label) by gas chromatography-mass spectrometry in selective ion monitoring (GC/MS-SIM) analysis. A key component involves the determination of the compositions of the most abundant naturally occurring isotopes of Cr (<sup>50</sup>Cr, <sup>52</sup>Cr, <sup>53</sup>Cr), and converting the proportions into a 3 × 3 matrix. To estimate unknown proportions of chromium isotopic mixtures from the measured abundances of three ions, an inverse matrix was calculated. The inverse together with several inputs is then used to calculate the corrected MS ion abundances. Thus, we constructed the software tool UHAS- MIDA using HTML, CSS/Bootstrap, JavaScript, and PHP scripting languages. The tool enables the user to efficiently determine RBC concentration and fluid volume. The source code, binary packages and associated materials for UHAS-MIDA are freely available at https://github.com/bentil078/Abaye-et-al_UHASmida
文摘This study focuses on estimating O-D （origin-destination） trip demand from link traffic flows. Equality relationship among link traffic flow, path flow, and O-D trip matrices are used to establish a linear equation system. Solution characteristics are analyzed based on the relationship between the rank of the link/path incidence matrix and column variables. And under the solution framework of conditional inverse matrices, a column exchange method and a path flow proportion method have been developed. Network testing results verify that the proposed methods yield good results.
