In this work we describe the algorithms to construct the skeletons, simplified 1D representations for a 3D surface depicted by a mesh of points, given the respective eigenfunctions of the Discrete Laplace-Beltrami Ope...In this work we describe the algorithms to construct the skeletons, simplified 1D representations for a 3D surface depicted by a mesh of points, given the respective eigenfunctions of the Discrete Laplace-Beltrami Operator (LBO). These functions are isometry invariant, so they are independent of the object’s representation including parameterization, spatial position and orientation. Several works have shown that these eigenfunctions provide topological and geometrical information of the surfaces of interest [1] [2]. We propose to make use of that information for the construction of a set of skeletons, associated to each eigenfunction, which can be used as a fingerprint for the surface of interest. The main goal is to develop a classification system based on these skeletons, instead of the surfaces, for the analysis of medical images, for instance.展开更多
We consider the following eigenvalue problem: [GRAPHICS] Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstat...The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.展开更多
The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow ...The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.展开更多
Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurati...Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.展开更多
In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-...In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.展开更多
Let{e_(j)}be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold(M,g).Let H■M be a submanifold and{ψ_(k)}be an orthonormal basis of Laplace eigenfunctions of H with the induced metric.We ...Let{e_(j)}be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold(M,g).Let H■M be a submanifold and{ψ_(k)}be an orthonormal basis of Laplace eigenfunctions of H with the induced metric.We obtain joint asymptotics for the Fourier coefficients<γHe_(j),ψ_(k)>L^(2)(H)=∫He_(j),ψ_(k)dV_(H)of restrictionsγHe_(j)of e_(j)to H.In particular,we obtain asymptotics for the sums of the norm-squares of the Fourier coefficients over the joint spectrum{(μ_(k),λ_(j))}^(∞)_(j,k-0)of the(square roots of the)Laplacian△_(M)on M and the Laplacian△_(H)on H in a family of suitably‘thick'regions in R^(2).Thick regions include(1)the truncated coneμ_(k)/λ_(j)∈[a,b]■(0,1)andλ_(j)≤λ,and(2)the slowly thickening strip|μ_(k)-cλ_(j)|≤w(λ)andλ_(j)≤λ,where w(λ)is monotonic and 1■w(λ)≤λ^(1/2).Key tools for obtaining the asymptotics include the composition calculus of Fourier integral operators and a new multidimensional Tauberian theorem.展开更多
The eigenfunctions in a stability problem of boundary-layer flow over a viscoelastic compliant wall were studied. Two categories of modes, TSI and CIFI, exist in the eigenvalue solutions. The eigenfunctions of flow-ba...The eigenfunctions in a stability problem of boundary-layer flow over a viscoelastic compliant wall were studied. Two categories of modes, TSI and CIFI, exist in the eigenvalue solutions. The eigenfunctions of flow-based TSI were investigated together with those in the flow over rigid wall, whereas the eigenfunctions of wall-based CIFI were compared with the wall functions in an individual wall without fluid constraint. The physical characteristics of the eigenmodes were discussed based on their eigenfunctions.展开更多
In this paper we shall consider the nonresonance Dirichlet boundary value problemwhere λ>0 is a parameter, p>0 is a constant. Intervals of A are determined to ensure the existence of a nonnegative solution of t...In this paper we shall consider the nonresonance Dirichlet boundary value problemwhere λ>0 is a parameter, p>0 is a constant. Intervals of A are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8].展开更多
We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenen...We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenenergies.The method is based on a generalized Brillouin-Wigner perturbation theory.Each flow is specific for a given energy and,at each step of the flow,a finite subspace of the Hilbert space is decimated in order to obtain a renormalized Hamiltonian for the next step.Eigenenergies of the original Hamiltonian appear as unstable fixed points of renormalized flows.Numerical illustration of the method is given in the Wigner-band random-matrix model.展开更多
Let L be the sublaplacian on the quaternion Heisenberg group N and T the Dirac type operator with respect to central variables of N. In this article, we characterize the He-valued joint eigenfunctions of L and T havin...Let L be the sublaplacian on the quaternion Heisenberg group N and T the Dirac type operator with respect to central variables of N. In this article, we characterize the He-valued joint eigenfunctions of L and T having eigenvalues from the quaternionic Heisenberg fan.展开更多
We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared ...We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave [unctions and the degree of degeneracy. By comparison, we refine A vinash Khare＇s results by making some items in his article precisely.展开更多
In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are mot...In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are motivated by physical problems including the determination of the extremum of the fundamental vibration frequency and the localization of the vibration displacement.We demonstrate how an iterative rearrangement approach and a gradient descent approach with projection can successfully solve these optimization problems under different boundary conditions with different densities given.展开更多
Global warming has led to major melting of ice in the polar Arctic,making it possible to open Arctic shipping lanes.In this case,the large number of ice sheets are extremely dangerous for ship navigation,so in this pa...Global warming has led to major melting of ice in the polar Arctic,making it possible to open Arctic shipping lanes.In this case,the large number of ice sheets are extremely dangerous for ship navigation,so in this paper,a body floating on water confined between two finite ice sheets is investigated.The linearized potential flow theory is adopted,and water is considered an incompressible ideal fluid with a finite depth of the fluid domain.The ice sheets are treated as elastic plates,and the problem is solved by matching eigenfunction expansion.The fluid domain is divided into subregions on the basis of the water surface conditions,and the velocity potential of the subdomains is expanded via the separated variable method.By utilizing the continuity of pressure and velocity at the interfaces of two neighboring regions,a system of linear equations is established to obtain the unknown coefficients in the expansion,which in turn leads to analytical solutions for different motion modes in different regions.The effects of different structural drafts,and different lengths of ice sheets on both sides,etc.,on the hydrodynamic characteristics of floats are analyzed.The amplitude of motion of the float is explored,as is the wave elevation between the ice sheets and the float.展开更多
The wave interaction with stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed based on the small amplitude wave theory.The study is performed to analyse the effect...The wave interaction with stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed based on the small amplitude wave theory.The study is performed to analyse the effectiveness of partial porous structure in increasing the wave attenuation in the nearshore regions consisting of stratified porous structures of different configurations using the eigenfunction expansion method and orthogonal mode-coupling relation.The hydrodynamic characteristics such as wave reflection coefficient,transmission coefficient,dissipation coefficient,wave force impact and surface elevation are investigated due to the presence of both horizontally and vertically stratified porous structures.The effect of varying porosity,structural width,angle of incidence,wavelength and length between the porous block and stratified structure is examined.The numerical results are validated with the results available in the literature.The present study illustrates that the presence of the stratified structure decreases wave transmission and efficient wave attenuation can also be easily achieved.The wave force acting on stratified structure can be decreased if the structure is combined with wider surface-piercing porous blocks.Further,the presence of stratified porous structure combined with porous block helps in creating a tranquil zone in the leeside of the structure.The combination of vertical and horizontal stratified porous structure with surface-piercing porous block is intended to be an effective solution for the protection of coastal facilities.展开更多
The Weber-Hermite differential equation, obtained as the dimensionless form of the stationary Schroedinger equation for a linear harmonic oscillator in quantum mechanics, has been expressed in a generalized form throu...The Weber-Hermite differential equation, obtained as the dimensionless form of the stationary Schroedinger equation for a linear harmonic oscillator in quantum mechanics, has been expressed in a generalized form through introduction of a constant conjugation parameter according to the transformation , where the conjugation parameter is set to unity () at the end of the evaluations. Factorization in normal order form yields composite eigenfunctions, Hermite polynomials and corresponding positive eigenvalues, while factorization in the anti-normal order form yields the partner composite anti-eigenfunctions, anti-Hermite polynomials and negative eigenvalues. The two sets of solutions are related by an reversal conjugation rule . Setting provides the standard Hermite polynomials and their partner anti-Hermite polynomials. The anti-Hermite polynomials satisfy a new differential equation, which is interpreted as the conjugate of the standard Hermite differential equation.展开更多
The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with pi...The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.展开更多
The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt&rarr0 is given first. When the continuous-time n-dimensional eigenvalue equatio...The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt&rarr0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has been reduced from the original 2n-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation Ae = eA. All the eigenvalues of Ae are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of Ae nearest to the unit circle can be calculated by the dual subspace iteration method.展开更多
In the airborne radar space-time adaptive processing (STAP), the interference covariance matrix must be estimated from the IID samples which are always limited in practice. Aimed at this problem, this paper studies th...In the airborne radar space-time adaptive processing (STAP), the interference covariance matrix must be estimated from the IID samples which are always limited in practice. Aimed at this problem, this paper studies the combination of the forward-backward averaging (FB), diagonal loading (DL) and the reduced-rank processing to reduce the required sample number as much as possible. Through analysis and simulations, it is demonstrated that by using proper reduced-rank processing, combined with FB and DL, the required sample number can be largely reduced to even 3-5 samples.展开更多
文摘In this work we describe the algorithms to construct the skeletons, simplified 1D representations for a 3D surface depicted by a mesh of points, given the respective eigenfunctions of the Discrete Laplace-Beltrami Operator (LBO). These functions are isometry invariant, so they are independent of the object’s representation including parameterization, spatial position and orientation. Several works have shown that these eigenfunctions provide topological and geometrical information of the surfaces of interest [1] [2]. We propose to make use of that information for the construction of a set of skeletons, associated to each eigenfunction, which can be used as a fingerprint for the surface of interest. The main goal is to develop a classification system based on these skeletons, instead of the surfaces, for the analysis of medical images, for instance.
文摘We consider the following eigenvalue problem: [GRAPHICS] Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
文摘The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.
文摘The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.
文摘Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.
基金The author is partially supported by the Nature Science Foundation of Guangdong(5012285)the"Thousand,Hundred,Ten"Science Foundation of Guangdong(Q02052)the Nature Science Foundation of Education Bureau of Guangdong(Z02075)
文摘In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.
基金supported by National Science Foundation of USA (Grant Nos.DMS-1810747 and DMS-1502632)supported by National Natural Science Foundation of China (Grant No.12171424)。
文摘Let{e_(j)}be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold(M,g).Let H■M be a submanifold and{ψ_(k)}be an orthonormal basis of Laplace eigenfunctions of H with the induced metric.We obtain joint asymptotics for the Fourier coefficients<γHe_(j),ψ_(k)>L^(2)(H)=∫He_(j),ψ_(k)dV_(H)of restrictionsγHe_(j)of e_(j)to H.In particular,we obtain asymptotics for the sums of the norm-squares of the Fourier coefficients over the joint spectrum{(μ_(k),λ_(j))}^(∞)_(j,k-0)of the(square roots of the)Laplacian△_(M)on M and the Laplacian△_(H)on H in a family of suitably‘thick'regions in R^(2).Thick regions include(1)the truncated coneμ_(k)/λ_(j)∈[a,b]■(0,1)andλ_(j)≤λ,and(2)the slowly thickening strip|μ_(k)-cλ_(j)|≤w(λ)andλ_(j)≤λ,where w(λ)is monotonic and 1■w(λ)≤λ^(1/2).Key tools for obtaining the asymptotics include the composition calculus of Fourier integral operators and a new multidimensional Tauberian theorem.
文摘The eigenfunctions in a stability problem of boundary-layer flow over a viscoelastic compliant wall were studied. Two categories of modes, TSI and CIFI, exist in the eigenvalue solutions. The eigenfunctions of flow-based TSI were investigated together with those in the flow over rigid wall, whereas the eigenfunctions of wall-based CIFI were compared with the wall functions in an individual wall without fluid constraint. The physical characteristics of the eigenmodes were discussed based on their eigenfunctions.
基金the National Natural Science Foundation of China (No.19871048)Natural Science Foundation of Shandong Province of China (No.Z2000A02, Y2001A03).
文摘In this paper we shall consider the nonresonance Dirichlet boundary value problemwhere λ>0 is a parameter, p>0 is a constant. Intervals of A are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8].
基金Supported by the National Natural Science Foundation of China under Grant Nos.11275179,11535011,and 11775210
文摘We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenenergies.The method is based on a generalized Brillouin-Wigner perturbation theory.Each flow is specific for a given energy and,at each step of the flow,a finite subspace of the Hilbert space is decimated in order to obtain a renormalized Hamiltonian for the next step.Eigenenergies of the original Hamiltonian appear as unstable fixed points of renormalized flows.Numerical illustration of the method is given in the Wigner-band random-matrix model.
基金supported by National Natural Science Foundation of China(Grant Nos.10871003 and 10990012)
文摘Let L be the sublaplacian on the quaternion Heisenberg group N and T the Dirac type operator with respect to central variables of N. In this article, we characterize the He-valued joint eigenfunctions of L and T having eigenvalues from the quaternionic Heisenberg fan.
基金Supported by the National Natural Science Foundation of China under Grant No.10975125
文摘We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave [unctions and the degree of degeneracy. By comparison, we refine A vinash Khare＇s results by making some items in his article precisely.
基金supported by the DMS-1853701supported in part by the DMS-2208373.
文摘In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are motivated by physical problems including the determination of the extremum of the fundamental vibration frequency and the localization of the vibration displacement.We demonstrate how an iterative rearrangement approach and a gradient descent approach with projection can successfully solve these optimization problems under different boundary conditions with different densities given.
文摘Global warming has led to major melting of ice in the polar Arctic,making it possible to open Arctic shipping lanes.In this case,the large number of ice sheets are extremely dangerous for ship navigation,so in this paper,a body floating on water confined between two finite ice sheets is investigated.The linearized potential flow theory is adopted,and water is considered an incompressible ideal fluid with a finite depth of the fluid domain.The ice sheets are treated as elastic plates,and the problem is solved by matching eigenfunction expansion.The fluid domain is divided into subregions on the basis of the water surface conditions,and the velocity potential of the subdomains is expanded via the separated variable method.By utilizing the continuity of pressure and velocity at the interfaces of two neighboring regions,a system of linear equations is established to obtain the unknown coefficients in the expansion,which in turn leads to analytical solutions for different motion modes in different regions.The effects of different structural drafts,and different lengths of ice sheets on both sides,etc.,on the hydrodynamic characteristics of floats are analyzed.The amplitude of motion of the float is explored,as is the wave elevation between the ice sheets and the float.
基金Science and Engineering Research Board(SERB),Department of Science&Technology(DST),Government of India for supporting financially under the research grant No.CRG/2018/004184Ministry of Ports,Shipping and Waterways,Government of India through the research grant No.DW/01013(13)/2/2021.
文摘The wave interaction with stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed based on the small amplitude wave theory.The study is performed to analyse the effectiveness of partial porous structure in increasing the wave attenuation in the nearshore regions consisting of stratified porous structures of different configurations using the eigenfunction expansion method and orthogonal mode-coupling relation.The hydrodynamic characteristics such as wave reflection coefficient,transmission coefficient,dissipation coefficient,wave force impact and surface elevation are investigated due to the presence of both horizontally and vertically stratified porous structures.The effect of varying porosity,structural width,angle of incidence,wavelength and length between the porous block and stratified structure is examined.The numerical results are validated with the results available in the literature.The present study illustrates that the presence of the stratified structure decreases wave transmission and efficient wave attenuation can also be easily achieved.The wave force acting on stratified structure can be decreased if the structure is combined with wider surface-piercing porous blocks.Further,the presence of stratified porous structure combined with porous block helps in creating a tranquil zone in the leeside of the structure.The combination of vertical and horizontal stratified porous structure with surface-piercing porous block is intended to be an effective solution for the protection of coastal facilities.
文摘The Weber-Hermite differential equation, obtained as the dimensionless form of the stationary Schroedinger equation for a linear harmonic oscillator in quantum mechanics, has been expressed in a generalized form through introduction of a constant conjugation parameter according to the transformation , where the conjugation parameter is set to unity () at the end of the evaluations. Factorization in normal order form yields composite eigenfunctions, Hermite polynomials and corresponding positive eigenvalues, while factorization in the anti-normal order form yields the partner composite anti-eigenfunctions, anti-Hermite polynomials and negative eigenvalues. The two sets of solutions are related by an reversal conjugation rule . Setting provides the standard Hermite polynomials and their partner anti-Hermite polynomials. The anti-Hermite polynomials satisfy a new differential equation, which is interpreted as the conjugate of the standard Hermite differential equation.
文摘The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.
文摘The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt&rarr0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has been reduced from the original 2n-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation Ae = eA. All the eigenvalues of Ae are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of Ae nearest to the unit circle can be calculated by the dual subspace iteration method.
文摘In the airborne radar space-time adaptive processing (STAP), the interference covariance matrix must be estimated from the IID samples which are always limited in practice. Aimed at this problem, this paper studies the combination of the forward-backward averaging (FB), diagonal loading (DL) and the reduced-rank processing to reduce the required sample number as much as possible. Through analysis and simulations, it is demonstrated that by using proper reduced-rank processing, combined with FB and DL, the required sample number can be largely reduced to even 3-5 samples.
