LSQR algorithm with structured preconditioner for the least squares problem in quaternionic quantum theory

DOI10.1016/j.camwa.2017.03.006zbMath1373.65029OpenAlexW2608086743MaRDI QIDQ2403829

Si-Tao Ling, Zhi-Gang Jia, Tong-Song Jiang

Publication date: 12 September 2017

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.03.006

zbMATH Keywords

algorithmconvergence accelerationreal representationiterative methodnumerical experimentleast squares problemquaternionic quantum theorystructured preconditionerincomplete inverse upper-lower factorizationsymmetric positive definite tridiagonal matrix

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items

Least-squares bihermitian and skew bihermitian solutions of the quaternion matrix equationAXB = C ⋮ A new implementation of LSMR algorithm for the quaternionic least squares problem ⋮ A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications ⋮ Matrix LSQR algorithm for structured solutions to quaternionic least squares problem

Uses Software

• LSQR
• SparseMatrix
• Quaternion
• CRAIG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two novel algebraic techniques for quaternion least squares problems in quaternionic quantum mechanics
• An algebraic method for quaternion and complex least squares coneigen-problem in quantum mechanics
• Algorithm Q-LSQR for the least squares problem in quaternionic quantum theory
• A comparative study of iterative solutions to linear systems arising in quantum mechanics
• Hermitian tridiagonal solution with the least norm to quaternionic least squares problem
• 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
• An improved preconditioned LSQR for discrete ill-posed problems
• Jacobi method for quaternion matrix singular value decomposition
• An algebraic technique for total least squares problem in quaternionic quantum theory
• A new technique of quaternion equality constrained least squares problem
• Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing
• Preconditioned GMRES methods with incomplete Givens orthogonalization method for large sparse least-squares problems
• Quaternionic electron theory: Dirac's equation
• Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics
• Subspace preconditioned LSQR for discrete ill-posed problems
• Equality constrained least squares problem over quaternion field
• Preconditioning techniques for large linear systems: A survey
• A new structure-preserving method for quaternion Hermitian eigenvalue problems
• The university of Florida sparse matrix collection
• Block Preconditioning for the Conjugate Gradient Method
• Recent computational developments in Krylov subspace methods for linear systems
• Block preconditioning of real-valued iterative algorithms for complex linear systems
• Quaternionic Representations of Compact Groups
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Factorized Sparse Approximate Inverse Preconditionings I. Theory
• Stability of Conjugate Gradient and Lanczos Methods for Linear Least Squares Problems
• A Robust Preconditioner with Low Memory Requirements for Large Sparse Least Squares Problems
• Quaternions and special relativity