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Vector Spaces of Linearizations for Matrix Polynomials
TLDR
This work develops a systematic approach to generating large classes of linearizations for a matrix polynomial, and shows how to simply construct two vector spaces of pencils that generalize the companion forms of $P, and proves that almost all of these pencils are linearized for $P$.
NLEVP: A Collection of Nonlinear Eigenvalue Problems
TLDR
NLEVP serves both to illustrate the tremendous variety of applications of nonlinear eigenvalue problems and to provide representative problems for testing, tuning, and benchmarking of algorithms and codes.
The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution
Notation and definitions.- Existence of solutions.- Eigenstructure of ?A - ?B, ?A? - ?B?.- Uniqueness and stability of feedback solutions.- Algebraic Riccati equations and deflating subspaces.-
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
TLDR
This paper analyzes the existence and uniqueness of a special class of linearizations which reflect the structure of structured polynomials, and therefore preserve symmetries in their spectra, and shows how they may be systematically constructed.
Numerical computation of an analytic singular value decomposition of a matrix valued function
SummaryThis paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of
SLICOT—A Subroutine Library in Systems and Control Theory
TLDR
This chapter describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory and builds methods for the design and analysis of linear control systems.
Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form
TLDR
This paper first gives a brief overview of the basic concepts from linear system theory and then presents balanced truncation model reduction methods for descriptor systems and discusses their algorithmic aspects.
Numerical methods for simultaneous diagonalization
TLDR
A Jacobi-like algorithm for simultaneous diagonalization of commuting pairs of complex normal matrices by unitary similarity transformations is presented, which preserves the special structure of real matrices, quaternion matrices and real symmetric matrices.
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