Hermitian tridiagonal solution with the least norm to quaternionic least squares problem

DOI10.1016/j.cpc.2009.10.019zbMath1205.81086OpenAlexW1983706988MaRDI QIDQ615084

Musheng Wei, Si-Tao Ling, Ming-hui Wang

Publication date: 5 January 2011

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2009.10.019

zbMATH Keywords

preconditioningLSQRquaternion matrixHermitian tridiagonal matrixquaternionic least squares

Mathematics Subject Classification ID

Least squares and related methods for stochastic control systems (93E24) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Computational methods for problems pertaining to quantum theory (81-08) Numerical approximation and computational geometry (primarily algorithms) (65D99)

Related Items (14)

Least-squares bihermitian and skew bihermitian solutions of the quaternion matrix equationAXB = C ⋮ Common solutions to some operator equations over HilbertC^*–modules and applications ⋮ LSQR algorithm with structured preconditioner for the least squares problem in quaternionic quantum theory ⋮ The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra ⋮ A new implementation of LSMR algorithm for the quaternionic least squares problem ⋮ The solution of a generalized Sylvester quaternion matrix equation and its application ⋮ An efficient method for solving a quaternionic least-squares problem ⋮ Matrix LSQR algorithm for structured solutions to quaternionic least squares problem ⋮ A real representation method for solving Yakubovich-\(j\)-conjugate quaternion matrix equation ⋮ Iterative algorithms for least-squares solutions of a quaternion matrix equation ⋮ New results on condensed Cramer's rule for the general solution to some restricted quaternion matrix equations ⋮ Special least squares solutions of the quaternion matrix equation \(AXB+CXD=E\) ⋮ The least square solution with the least norm to a system of quaternion matrix equations ⋮ Cramer's rules for various solutions to some restricted quaternionic linear systems

Uses Software

• LSQR
• CRAIG

Cites Work

• Algebraic algorithms for least squares problem in quaternionic quantum theory
• An algebraic method for Schrödinger equations in quaternionic quantum mechanics
• An iterative algorithm for least squares problem in quaternionic quantum theory
• A new technique of quaternion equality constrained least squares problem
• Analytic solution of the wave equation for an electron in the field of a molecule with an electric dipole moment
• Quaternionic quantum field theory
• Equality constrained least squares problem over quaternion field
• Gaussian ensemble of tridiagonal symmetric random matrices.
• Condition numbers and equilibration of matrices
• Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Analytical inversion of symmetric tridiagonal matrices
• The analytic inversion of any finite symmetric tridiagonal matrix
• Some Theorems On Matrices With Real Quaternion Elements

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