Journal of approximation theory, ISSN 0021-9045, 2017, Volume 216, pp. 38 - 66

We study the asymptotics of generalized eigenvectors associated with Jacobi matrices...

Total variation | Jacobi matrix | Asymptotics of generalized eigenvectors | MATHEMATICS | EIGENVALUES | ORDER | ORTHOGONAL POLYNOMIALS | SPECTRAL PROPERTIES

Total variation | Jacobi matrix | Asymptotics of generalized eigenvectors | MATHEMATICS | EIGENVALUES | ORDER | ORTHOGONAL POLYNOMIALS | SPECTRAL PROPERTIES

Journal Article

Zeitschrift fur Analysis und ihre Anwendung, ISSN 0232-2064, 2009, Volume 28, Issue 4, pp. 411 - 430

This paper is concerned with asymptotic behavior of generalized eigenvectors of a class of Hermitian Jacobi matrices J in the critical case...

Jacobi matrix | Subordinacy theory | WKB asymptotics | Generalized eigenvector | Asymptotic behavior of solutions | Spectrum | subordinacy theory | MATHEMATICS, APPLIED | UNIFORM | asymptotic behavior of solutions | SUBORDINACY | SPECTRAL PROPERTIES | MATHEMATICS | EIGENVALUES | spectrum | THEOREMS | BIRTH | OPERATORS

Jacobi matrix | Subordinacy theory | WKB asymptotics | Generalized eigenvector | Asymptotic behavior of solutions | Spectrum | subordinacy theory | MATHEMATICS, APPLIED | UNIFORM | asymptotic behavior of solutions | SUBORDINACY | SPECTRAL PROPERTIES | MATHEMATICS | EIGENVALUES | spectrum | THEOREMS | BIRTH | OPERATORS

Journal Article

Journal of computational physics, ISSN 0021-9991, 2018, Volume 375, pp. 1238 - 1269

The Riemann problem, and the associated generalized Riemann problem, are increasingly seen as the important building blocks for modern higher order Godunov-type schemes...

Hyperbolic conservation laws | Stiff sources | Generalized Riemann problem solver | Non-conservative hyperbolic problems | HLLI Riemann solver | DISCONTINUOUS GALERKIN SCHEMES | HYPERBOLIC SYSTEMS | ASYMPTOTIC-EXPANSION | EQUATIONS | IMPLEMENTATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EULERIAN GRP SCHEME | ADER SCHEMES | GODUNOV-TYPE METHODS | FINITE-VOLUME SCHEMES | PIECEWISE PARABOLIC METHOD | Environmental law | Mathematical problems | Energy dissipation | Conservation | Problem solving | Eigenvectors | Computational physics | Hyperbolic systems | Riemann solver | Eigen values | Mathematics - Numerical Analysis

Hyperbolic conservation laws | Stiff sources | Generalized Riemann problem solver | Non-conservative hyperbolic problems | HLLI Riemann solver | DISCONTINUOUS GALERKIN SCHEMES | HYPERBOLIC SYSTEMS | ASYMPTOTIC-EXPANSION | EQUATIONS | IMPLEMENTATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EULERIAN GRP SCHEME | ADER SCHEMES | GODUNOV-TYPE METHODS | FINITE-VOLUME SCHEMES | PIECEWISE PARABOLIC METHOD | Environmental law | Mathematical problems | Energy dissipation | Conservation | Problem solving | Eigenvectors | Computational physics | Hyperbolic systems | Riemann solver | Eigen values | Mathematics - Numerical Analysis

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2015, Volume 56, Issue 10, p. 103508

We demonstrate that not all generalized Bogoliubov transformations lead to D-pseudo-bosons and prove that a correspondence between the two can only be achieved with the imposition of specific...

SPECTRA | PHYSICS, MATHEMATICAL | NON-HERMITIAN HAMILTONIANS | Parameters | Asymptotic properties | Space bases | Norms | Transformations | Hilbert space | Eigenvectors | Quantum theory | Bosons

SPECTRA | PHYSICS, MATHEMATICAL | NON-HERMITIAN HAMILTONIANS | Parameters | Asymptotic properties | Space bases | Norms | Transformations | Hilbert space | Eigenvectors | Quantum theory | Bosons

Journal Article

Engineering Fracture Mechanics, ISSN 0013-7944, 02/2019, Volume 206, pp. 375 - 391

•The elastic stochastic isotropic solution in the vicinity of a crack is addressed.•The eigen-functions & displacements are approximated using the GPC...

Stochastic stress intensity factors | Generalized polynomial chaos | MECHANICS | PROBABILISTIC FRACTURE-MECHANICS | Monte Carlo method | Economic models | Crack tips | Computer simulation | Numerical methods | Boundary conditions | Modulus of elasticity | Poissons ratio | Finite element method | Asymptotic series | Stress intensity factors | Normal distribution | Eigenvalues | Polynomials | Eigenvectors | Random variables | Isotropic material | Material properties

Stochastic stress intensity factors | Generalized polynomial chaos | MECHANICS | PROBABILISTIC FRACTURE-MECHANICS | Monte Carlo method | Economic models | Crack tips | Computer simulation | Numerical methods | Boundary conditions | Modulus of elasticity | Poissons ratio | Finite element method | Asymptotic series | Stress intensity factors | Normal distribution | Eigenvalues | Polynomials | Eigenvectors | Random variables | Isotropic material | Material properties

Journal Article

Numerical Algorithms, ISSN 1017-1398, 3/2019, Volume 80, Issue 3, pp. 937 - 955

.... Under certain conditions, there is a simple generalized eigenvalue ρ(A, B) in the interval (0, 1) with a positive eigenvector...

M-matrix | Quadratic convergence | Generalized eigenproblem | Nonnegative irreducible matrix | Numeric Computing | Theory of Computation | Perron-Frobenius theory | Algorithms | Algebra | Generalized Noda iteration | 65F99 | Numerical Analysis | Computer Science | 65F15 | EIGENVALUE | MATHEMATICS, APPLIED | INVERSE ITERATION | Analysis

M-matrix | Quadratic convergence | Generalized eigenproblem | Nonnegative irreducible matrix | Numeric Computing | Theory of Computation | Perron-Frobenius theory | Algorithms | Algebra | Generalized Noda iteration | 65F99 | Numerical Analysis | Computer Science | 65F15 | EIGENVALUE | MATHEMATICS, APPLIED | INVERSE ITERATION | Analysis

Journal Article

7.
Full Text
Green Matrix Estimates of Block Jacobi Matrices I: Unbounded Gap in the Essential Spectrum

Integral equations and operator theory, ISSN 1420-8989, 2018, Volume 90, Issue 4, pp. 1 - 24

This work deals with decay bounds for Green matrices and generalized eigenvectors of block Jacobi matrices when the real part of the spectral parameter lies in an infinite gap...

39A22 | 47B36 | 33E30 | Analysis | Decay bounds | Mathematics | Block Jacobi operators | Generalized eigenvectors | MATHEMATICS | LOCALIZATION | SCHRODINGER-OPERATORS | ASYMPTOTIC-BEHAVIOR

39A22 | 47B36 | 33E30 | Analysis | Decay bounds | Mathematics | Block Jacobi operators | Generalized eigenvectors | MATHEMATICS | LOCALIZATION | SCHRODINGER-OPERATORS | ASYMPTOTIC-BEHAVIOR

Journal Article

International Journal of Intelligent Systems, ISSN 0884-8173, 03/2013, Volume 28, Issue 3, pp. 289 - 306

We consider adaptively extracting multiple principal generalized eigenvectors, which can be widely applied in modern signal processing...

matrix pencil | generalized eigen‐decomposition | Newton method | Generalized eigenvector | neural networks | generalized eigen-decomposition | EIGENDECOMPOSITION | SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms | Studies | Approximation | Computer simulation | Neural networks | Asymptotic properties | Mathematical analysis | Adaptive algorithms | Eigenvectors

matrix pencil | generalized eigen‐decomposition | Newton method | Generalized eigenvector | neural networks | generalized eigen-decomposition | EIGENDECOMPOSITION | SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms | Studies | Approximation | Computer simulation | Neural networks | Asymptotic properties | Mathematical analysis | Adaptive algorithms | Eigenvectors

Journal Article

Probability theory and related fields, ISSN 1432-2064, 2011, Volume 155, Issue 3-4, pp. 543 - 582

.... We prove that the joint probability distribution of the components of eigenvectors associated with eigenvalues close to the spectral edge agrees with that of the corresponding Gaussian ensemble...

Eigenvector distribution | 15B52 | Random matrix | 82B44 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | Universality | Quantitative Finance | EIGENVALUES | RESPECT | DELOCALIZATION | SEMICIRCLE LAW | STATISTICS & PROBABILITY | ORTHOGONAL POLYNOMIALS | ASYMPTOTICS | SPECTRUM | EDGE | Studies | Normal distribution | Analysis | Eigen values | Mathematical analysis | Edge joints | Eigenvalues | Eigenvectors | Gaussian | Matrices | Spectra | Matrix methods

Eigenvector distribution | 15B52 | Random matrix | 82B44 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | Universality | Quantitative Finance | EIGENVALUES | RESPECT | DELOCALIZATION | SEMICIRCLE LAW | STATISTICS & PROBABILITY | ORTHOGONAL POLYNOMIALS | ASYMPTOTICS | SPECTRUM | EDGE | Studies | Normal distribution | Analysis | Eigen values | Mathematical analysis | Edge joints | Eigenvalues | Eigenvectors | Gaussian | Matrices | Spectra | Matrix methods

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2011, Volume 227, Issue 1, pp. 494 - 521

We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices...

Random matrices | Random perturbation | Free probability | Haar measure | Principal components analysis | Random eigenvectors | Informational limit | Sample covariance matrices | Random eigenvalues | Phase transition | Randomeigenvectors | LIMIT | DEFORMATION | CONVOLUTION | MATHEMATICS | RESPECT | LARGE WIGNER MATRICES | ASYMPTOTICS

Random matrices | Random perturbation | Free probability | Haar measure | Principal components analysis | Random eigenvectors | Informational limit | Sample covariance matrices | Random eigenvalues | Phase transition | Randomeigenvectors | LIMIT | DEFORMATION | CONVOLUTION | MATHEMATICS | RESPECT | LARGE WIGNER MATRICES | ASYMPTOTICS

Journal Article

Constructive approximation, ISSN 1432-0940, 2018, Volume 48, Issue 2, pp. 301 - 335

.... Uniform asymptotics of generalized eigenvectors and conditions implying complete indeterminacy are also provided.

Primary: 47B25 | 47B36 | Numerical Analysis | Analysis | Block Jacobi matrix | Total variation | Mathematics | Asymptotics of generalised eigenvectors | 42C05 | POLYNOMIALS | MATHEMATICS | ORDER | PERIODIC PERTURBATIONS | ASYMPTOTICS

Primary: 47B25 | 47B36 | Numerical Analysis | Analysis | Block Jacobi matrix | Total variation | Mathematics | Asymptotics of generalised eigenvectors | 42C05 | POLYNOMIALS | MATHEMATICS | ORDER | PERIODIC PERTURBATIONS | ASYMPTOTICS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2014, Volume 55, Issue 10, p. 102105

We present that N-dimensional non-relativistic wave equation for the generalized non-central potential with arbitrary angular momentum is analytically solvable in the hyperspherical coordinates...

KLEIN-GORDON EQUATION | ARBITRARY DIMENSIONS | QUANTUM-MECHANICAL OSCILLATOR | ORBITAL ANGULAR MOMENTUM | PATH-INTEGRAL SOLUTION | HARMONIC-OSCILLATOR | SCHRODINGER-EQUATION | HYDROGEN-ATOM | DEGENERATE OSCILLATOR | PHYSICS, MATHEMATICAL | ASYMPTOTIC ITERATION METHOD | Hypergeometric functions | Mathematical analysis | Angular momentum | Wave equations | Eigenvalues | Polynomials | Eigenvectors | Asymptotic methods | POLYNOMIALS | ANGULAR MOMENTUM | EIGENVALUES | HYPERGEOMETRIC FUNCTIONS | WAVE EQUATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CENTRAL POTENTIAL | EIGENFUNCTIONS | CURVILINEAR COORDINATES | ANALYTICAL SOLUTION

KLEIN-GORDON EQUATION | ARBITRARY DIMENSIONS | QUANTUM-MECHANICAL OSCILLATOR | ORBITAL ANGULAR MOMENTUM | PATH-INTEGRAL SOLUTION | HARMONIC-OSCILLATOR | SCHRODINGER-EQUATION | HYDROGEN-ATOM | DEGENERATE OSCILLATOR | PHYSICS, MATHEMATICAL | ASYMPTOTIC ITERATION METHOD | Hypergeometric functions | Mathematical analysis | Angular momentum | Wave equations | Eigenvalues | Polynomials | Eigenvectors | Asymptotic methods | POLYNOMIALS | ANGULAR MOMENTUM | EIGENVALUES | HYPERGEOMETRIC FUNCTIONS | WAVE EQUATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CENTRAL POTENTIAL | EIGENFUNCTIONS | CURVILINEAR COORDINATES | ANALYTICAL SOLUTION

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 06/2006, Volume 12, Issue 6, pp. 597 - 618

This paper presents two methods of finding asymptotic formulae for a basis of solutions of the second order difference equations in the Jordan box case. An...

Non-oscillatory solution | Difference equation | Jacobi operator | Spectral analysis | Asymptotic behavior | Jordan box | difference equation | MATHEMATICS, APPLIED | asymptotic behavior | non-oscillatory solution | MATRICES | spectral analysis | SPECTRAL PROPERTIES

Non-oscillatory solution | Difference equation | Jacobi operator | Spectral analysis | Asymptotic behavior | Jordan box | difference equation | MATHEMATICS, APPLIED | asymptotic behavior | non-oscillatory solution | MATRICES | spectral analysis | SPECTRAL PROPERTIES

Journal Article

International Journal of Modern Physics E, ISSN 0218-3013, 10/2012, Volume 21, Issue 10, pp. 1250087 - 1250012

The analytical expressions for the eigenvalues and eigenvectors of the Klein–Gordon equation for q-deformed Woods...

MATRIX | SPIN | V(X) | SCHRODINGER-EQUATION | PHYSICS, NUCLEAR | asymptotic iteration method | DIRAC | NUCLEI | EIGENENERGIES | Klein-Gordon equation | q-deformed Woods-Saxon potential | ring-shaped potential | PHYSICS, PARTICLES & FIELDS | Asymptotic properties | Mathematical analysis | Exact solutions | Eigenvalues | Scalars | Eigenvectors | Vectors (mathematics)

MATRIX | SPIN | V(X) | SCHRODINGER-EQUATION | PHYSICS, NUCLEAR | asymptotic iteration method | DIRAC | NUCLEI | EIGENENERGIES | Klein-Gordon equation | q-deformed Woods-Saxon potential | ring-shaped potential | PHYSICS, PARTICLES & FIELDS | Asymptotic properties | Mathematical analysis | Exact solutions | Eigenvalues | Scalars | Eigenvectors | Vectors (mathematics)

Journal Article

IEEE transactions on signal processing, ISSN 1941-0476, 2019, Volume 67, Issue 12, pp. 3287 - 3299

This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices...

Symmetric matrices | Correlation | power method | Chebyshev polynomial | Complexity theory | generalized eigenvalue (GEV) problems | stochastic convex optimization | Signal processing algorithms | Approximation algorithms | canonical correlation analysis (CCA) | Eigenvalues and eigenfunctions | Approximation theory | Acceleration | ENGINEERING, ELECTRICAL & ELECTRONIC | Asymptotic methods | Matrix methods | Optimization | Computational geometry | Algorithms | Mathematical analysis | Run time (computers) | Correlation analysis | Solvers | Eigenvectors | Convexity | Iterative methods

Symmetric matrices | Correlation | power method | Chebyshev polynomial | Complexity theory | generalized eigenvalue (GEV) problems | stochastic convex optimization | Signal processing algorithms | Approximation algorithms | canonical correlation analysis (CCA) | Eigenvalues and eigenfunctions | Approximation theory | Acceleration | ENGINEERING, ELECTRICAL & ELECTRONIC | Asymptotic methods | Matrix methods | Optimization | Computational geometry | Algorithms | Mathematical analysis | Run time (computers) | Correlation analysis | Solvers | Eigenvectors | Convexity | Iterative methods

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 05/2014, Volume 140, Issue 18, p. 18A541

A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the...

OPTIMIZED POTENTIAL METHOD | FRACTIONALLY OCCUPIED STATES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CORRELATION-ENERGY | INTEGER DISCONTINUITY | ATOMS | FORMALISM | EXCHANGE | EXACTLY SOLUBLE MODEL | GENERALIZED GRADIENT APPROXIMATION | EXCITED-STATES | Density functional theory | Eigenvectors | Charge transfer | Asymptotic properties | Electrons | Physics - Chemical Physics | DENSITY | EXCITED STATES | EXCITATION | TRIPLETS | DENSITY FUNCTIONAL METHOD | ELECTRONS | EIGENSTATES | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY

OPTIMIZED POTENTIAL METHOD | FRACTIONALLY OCCUPIED STATES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CORRELATION-ENERGY | INTEGER DISCONTINUITY | ATOMS | FORMALISM | EXCHANGE | EXACTLY SOLUBLE MODEL | GENERALIZED GRADIENT APPROXIMATION | EXCITED-STATES | Density functional theory | Eigenvectors | Charge transfer | Asymptotic properties | Electrons | Physics - Chemical Physics | DENSITY | EXCITED STATES | EXCITATION | TRIPLETS | DENSITY FUNCTIONAL METHOD | ELECTRONS | EIGENSTATES | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 2/2016, Volume 164, Issue 1, pp. 459 - 552

.... We investigate the principal components, i.e. the top eigenvalues and eigenvectors, of $${\mathcal {Q}}$$ Q . We derive precise large deviation estimates on the generalized components...

15B52 | 82B44 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Operation Research/Decision Theory | Quantitative Finance | UNIVERSALITY | AIRY KERNEL | PERTURBATIONS | LARGEST EIGENVALUE | FLUCTUATIONS | ENSEMBLES | STATISTICS & PROBABILITY | GENERALIZED WIGNER MATRICES | FINITE RANK DEFORMATIONS | RANDOM BAND MATRICES | SPIKED POPULATION-MODEL | Studies | Mathematical analysis | Eigen values | Covariance | Outliers (statistics) | Asymptotic properties | Eigenvalues | Texts | Eigenvectors | Deviation | Convergence

15B52 | 82B44 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Operation Research/Decision Theory | Quantitative Finance | UNIVERSALITY | AIRY KERNEL | PERTURBATIONS | LARGEST EIGENVALUE | FLUCTUATIONS | ENSEMBLES | STATISTICS & PROBABILITY | GENERALIZED WIGNER MATRICES | FINITE RANK DEFORMATIONS | RANDOM BAND MATRICES | SPIKED POPULATION-MODEL | Studies | Mathematical analysis | Eigen values | Covariance | Outliers (statistics) | Asymptotic properties | Eigenvalues | Texts | Eigenvectors | Deviation | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2020, Volume 190, p. 111614

In this paper, a nonhomogeneous eigenvalue problem with p-Laplacian is studied. We first show the Sturm–Liouville property and derive the asymptotic expansion...

Basis property | Ambarzumyan problem | Nonhomogeneous eigenvalue problem | [formula omitted]-Laplacian | Inverse nodal problem | MATHEMATICS | MATHEMATICS, APPLIED | p-Laplacian | FLUID | Inverse problems | Asymptotic series | Asymptotic properties | Eigenvalues | Eigenvectors | Trigonometric functions | Eigen values

Basis property | Ambarzumyan problem | Nonhomogeneous eigenvalue problem | [formula omitted]-Laplacian | Inverse nodal problem | MATHEMATICS | MATHEMATICS, APPLIED | p-Laplacian | FLUID | Inverse problems | Asymptotic series | Asymptotic properties | Eigenvalues | Eigenvectors | Trigonometric functions | Eigen values

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 08/2013, Volume 19, Issue 8, pp. 1251 - 1267

... small', for the case when has zero eigenvalue. We use this result to obtain estimates for some generalized eigenvectors of Jacobi operators...

linear systems of difference equations | the Levinson theorem | generalized eigenvectors | asymptotic behaviour of solutions | discrete and point spectrum | spectral analysis of Jacobi operators/matrices | MATHEMATICS, APPLIED | PERTURBATIONS | spectral analysis of Jacobi operators | matrices | SPECTRAL PROPERTIES | Operators | Theorems | Perturbation methods | Images | Decay | Eigenvalues | Eigenvectors | Estimates

linear systems of difference equations | the Levinson theorem | generalized eigenvectors | asymptotic behaviour of solutions | discrete and point spectrum | spectral analysis of Jacobi operators/matrices | MATHEMATICS, APPLIED | PERTURBATIONS | spectral analysis of Jacobi operators | matrices | SPECTRAL PROPERTIES | Operators | Theorems | Perturbation methods | Images | Decay | Eigenvalues | Eigenvectors | Estimates

Journal Article

Probability theory and related fields, ISSN 1432-2064, 2010, Volume 151, Issue 1-2, pp. 233 - 264

... N almost surely converges to some limiting probability distribution as N → ∞ and p/N → γ > 0. We quantify the relationship between sample and population eigenvectors by studying the asymptotics of functionals of the type...

Sample covariance matrix | Random matrix theory | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Shrinkage estimator | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Asymptotic distribution | Quantitative Finance | 15B52 | Bias correction | Eigenvectors and eigenvalues | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 62J10 | Principal component analysis | Stieltjes transform | THEOREM | LIMITING SPECTRAL DISTRIBUTION | STATISTICS & PROBABILITY | EMPIRICAL DISTRIBUTION | EIGENVALUES | DIMENSIONAL RANDOM MATRICES | CONVERGENCE | Studies | Normal distribution | Mathematical analysis | Asymptotic methods | Eigen values

Sample covariance matrix | Random matrix theory | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Shrinkage estimator | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Asymptotic distribution | Quantitative Finance | 15B52 | Bias correction | Eigenvectors and eigenvalues | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 62J10 | Principal component analysis | Stieltjes transform | THEOREM | LIMITING SPECTRAL DISTRIBUTION | STATISTICS & PROBABILITY | EMPIRICAL DISTRIBUTION | EIGENVALUES | DIMENSIONAL RANDOM MATRICES | CONVERGENCE | Studies | Normal distribution | Mathematical analysis | Asymptotic methods | Eigen values

Journal Article