Fast and stable algorithms for computing the principal \(n\)th root of a complex matrix and the matrix sector function

DOI10.1016/0898-1221(88)90034-XzbMath0653.65031MaRDI QIDQ1107951

R. E. Yates, Leang San Shieh, Jason Sheng-Hong Tsai

Publication date: 1988

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

numerical stabilitymatrix sector functionfast and stable recursive algorithmsprincipal n-th root of a complex matrix

Mathematics Subject Classification ID

Related Items (21)

Modelling of multirate feedback systems using uniform-rate models ⋮ An alternative digital redesign of continuous-time suboptimal regulators for input time-delay systems ⋮ Model conversion and digital redesign of singular systems ⋮ Digital modelling, ideal state reconstructor, and control for time-delay sampled-data systems ⋮ Determination of a matrix function using the divided difference method of Newton and the interpolation technique of Hermite ⋮ Block power method for computing solvent and spectral factors of matrix polynomials ⋮ Hybrid suboptimal control of multi-rate multi-loop sampled-data systems ⋮ Implementation of state-feedback control law for singular systems via an input-output feedback structure ⋮ Continuous to discrete model conversion for the system with a singular system matrix based on matrix sign function ⋮ Regions of convergence of a Padé family of iterations for the matrix sector function and the matrix \(p\)th root ⋮ Two-stage suboptimal discrete-time regulators for continuous-time stiff dynamic systems ⋮ Two-dimensional discrete-continuous model conversion ⋮ A computer-aided method for solvents and spectral factors of matrix polynomials ⋮ Low‐order multi‐rate linear time‐invariant decentralized trackers using the new observer‐based sub‐optimal method for unknown sampled‐data nonlinear time‐delay system with closed‐loop decoupling ⋮ A numerical study of fractional linear algebraic systems ⋮ Inversion free algorithms for computing the principal square root of a matrix ⋮ Residual methods for the large-scale matrix \(p\)th root and some related problems ⋮ A parallel algorithm for principal \(n\)th roots of matrices ⋮ Algorithms for the matrix \(p\)th root ⋮ Linear quadratic Nash game-based tracker for multiparameter singularly perturbed sampled-data systems: digital redesign approach ⋮ Generalized fractional algebraic linear system solvers

Cites Work

• Computation of roots of real and complex matrices
• A fast method for computing the principal \(n\)-th roots of complex matrices
• Roots of real matrices
• The matrix sign function and computations in systems
• A faster, more stable method for comuting the pth roots of positive definite matrices
• Fast and stable algorithms for computing the principal square root of a complex matrix
• Fast suboptimal state-space self-tuner for linear stochastic multivariable systems
• Some properties of matrix sign functions derived from continued fractions
• Matrix sector functions and their applications to systems theory
• The Generalized Matrix Sector Function and the Separation of Matrix Eigenvalues
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• A faster method of computing the square root of a matrix
• Newton's Method for the Matrix Square Root
• Computation of the principal nth roots of complex matrices

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