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Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2019, Volume 42, Issue 11, pp. 3791 - 3798
Cai and Zhang establish separate perturbation bounds for sinΘ distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for... 
norms of matrices | singular values | perturbation bounds | optimality | projection matrix | MATHEMATICS, APPLIED | Norms | Subspaces | Perturbation
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2018, Volume 540, pp. 26 - 59
Matrix perturbation inequalities, such as Weyl's theorem (concerning the singular values) and the Davis–Kahan theorem (concerning the singular vectors), play... 
Singular values | Singular vectors | Random perturbation | Random matrix | Singular value decomposition | MATHEMATICS, APPLIED | INEQUALITIES | NOISE | RANDOM-VARIABLES | GRAPHS | MATHEMATICS | PENALIZATION | NORM | COMPLETION | ENTRIES
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2019, Volume 2019, Issue 1, pp. 1 - 10
Rank-one perturbation of arbitrary matrices has many practical applications. In this paper, based on the relationship between the singular values and the... 
Singular values | Rank-one update | Arbitrary matrix | Eigenvalue gap | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | Perturbation methods | Eigenvalues
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 12/2017, Volume 534, pp. 135 - 157
For any n×n complex matrix A, let Ag be the group inverse of A. When A is singular, a matrix B=A+E is said to be an acute perturbation of A, if ‖E‖ is small... 
Upper bound | Oblique projection | Group inverse | Spectral radius | Acute perturbation | MATHEMATICS, APPLIED | SEMIITERATIVE METHODS | STATIONARY DISTRIBUTION | STABLE PERTURBATION | DRAZIN-INVERSE | MATHEMATICS | BOUNDS | GROUP GENERALIZED INVERSE | ERROR ANALYSIS | FINITE MARKOV-CHAINS | SINGULAR LINEAR-SYSTEMS
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 09/2018, Volume 58, Issue 3, pp. 599 - 612
In this paper, we present some uniform relative perturbation bounds for eigenvalues and eigenspaces of diagonalizable matrices under additive and... 
Additive perturbation bound | Diagonalizable matrix | Multiplicative perturbation bound | Eigenpair | EIGENVALUE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SINGULAR-VALUE DECOMPOSITIONS | EIGENSPACES | EIGENSYSTEMS | HERMITIAN MATRICES
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 01/2019, Volume 87, pp. 108 - 114
With weighted orthogonal Jacobi polynomials, we study spectral approximations for singular perturbation problems on an interval. The singular parameters of the... 
Spectral approximation | A posteriori error estimate | Singular perturbation problem | Generalized Jacobi polynomial | POLYNOMIALS | MATHEMATICS, APPLIED | 2ND-ORDER DIFFERENTIAL-EQUATIONS | SUPERCONVERGENCE | FINITE-ELEMENT | COLLOCATION METHODS
Journal Article
IEEE Transactions on Systems, Man, and Cybernetics: Systems, ISSN 2168-2216, 12/2018, Volume 48, Issue 12, pp. 2058 - 2069
This paper is concerned with the nonfragile H ∞ control problem for discrete-time fast sampling Markovian jump singularly perturbed nonlinear systems described... 
Fuzzy Markovian jump systems | mixed H∞ and passive control | singularly perturbed systems (SPSs) | nonfragile controller | Perturbation theory | Fuzzy control | Perturbation methods | Upper bounds | Singular perturbation | Tunnel diodes | Markov models | Conditioning | Sampling | Nonlinear systems | Fuzzy systems
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 05/2015, Volume 63, Issue 5, pp. 1037 - 1048
Based on the singular value decomposition, we obtain new multiplicative perturbation bounds of the Moore-Penrose inverse under the Frobenius norm, the... 
multiplicative perturbation bound | 15A24 | Moore-Penrose inverse | 15A09 | singular value decomposition | Moore–Penrose inverse | MATHEMATICS | LEAST-SQUARES PROBLEMS | Algebra | Images | Norms | Inverse | Decomposition | Perturbation | Invariants | Optimization
Journal Article
Numerical Algorithms, ISSN 1017-1398, 10/2018, Volume 79, Issue 2, pp. 657 - 677
In this paper, we consider the perturbation of the orthogonal projection and the generalized inverse for an n × n matrix A and present some perturbation bounds... 
Orthogonal projection | Algorithms | Algebra | 65F10 | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Perturbation | Generalized inverse | Singular value decomposition | DECOMPOSITIONS | MATHEMATICS, APPLIED
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 11
Perturbation bounds for eigenvalues of diagonalizable matrices are derived. Perturbation bounds for singular values of arbitrary matrices are also given. We... 
diagonalizable matrix | perturbation bound | eigenvalue | singular value | MATHEMATICS | MATHEMATICS, APPLIED | Eigenvalues | Inequalities | Perturbation
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2018, Volume 464, Issue 2, pp. 1010 - 1050
We introduce a new method to reformulate certain classes of problems involving non-local terms as local problems. This allows us to apply the techniques... 
Gamma-limit | Singular perturbation functional | Non-locality | SHARP UPPER-BOUNDS | MATHEMATICS | MATHEMATICS, APPLIED | OPTIMAL PROFILES | CONVERGENCE
Journal Article
International Journal of Applied and Computational Mathematics, ISSN 2349-5103, 12/2018, Volume 4, Issue 6, pp. 1 - 9
In this paper, some new relative perturbation bounds for the eigenvalues of diagonalizable matrices are derived. A relative perturbation bound for singular... 
Diagonalizable matrix | Theoretical, Mathematical and Computational Physics | Singular value | Eigenvalue | Mathematics | Computational Science and Engineering | 15A18 | 15A42 | Operations Research/Decision Theory | Nuclear Energy | 65F15 | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Perturbation bound
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2008, Volume 30, Issue 2, pp. 762 - 776
We derive absolute perturbation bounds for the coefficients of the characteristic polynomial of a n x n complex matrix. The bounds consist of elementary... 
Elementary symmetric functions | Condition number | Eigenvalues | Singular values | Determinant | MATHEMATICS, APPLIED | eigenvalues | singular values | condition number determinant | elementary symmetric functions
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 419, Issue 2, pp. 765 - 771
Perturbation bounds for the relative error in the eigenvalues of diagonalizable and singular matrices are derived by using perturbation theory for simple... 
Separation function | Relative perturbation bound | Simple invariant subspaces | Diagonalizable and singular matrix | MATHEMATICS, APPLIED | relative perturbation bound | simple invariant subspaces | separation function | diagonalizable and singular matrix
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 07/2019, Volume 353, pp. 295 - 307
In this article we study balanced model reduction of linear control systems using the singular perturbation approximation. Balanced model reduction techniques... 
Balanced truncation | Error bound | L2 norm | Singular perturbation approximation | Homogeneous and non-homogeneous initial conditions | norm | L-2 norm | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | PREDICTIVE CONTROL | NONLINEAR-SYSTEMS | ORDER REDUCTION | TRUNCATION | Control systems | Analysis
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 01/2013, Volume 58, Issue 1, pp. 168 - 174
Journal Article
Mathematics, ISSN 2227-7390, 10/2018, Volume 6, Issue 11, p. 232
In this article, we present up to date results on the balanced model reduction techniques for linear control systems, in particular the singular perturbation... 
Error bound | Reciprocal system | Singular perturbation approximation | Non-homogeneous system | MATHEMATICS | VISCOSITY SOLUTIONS | error bound | singular perturbation approximation | non-homogeneous system | reciprocal system
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 04/2016, Volume 64, Issue 4, pp. 622 - 652
Journal Article
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