Structure Preserving Quaternion Generalized Minimal Residual Method

DOI10.1137/20M133751XzbMath1468.65030OpenAlexW3153688434MaRDI QIDQ4986831

Zhi-Gang Jia, Michael Kwok-Po Ng

Publication date: 28 April 2021

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m133751x

zbMATH Keywords

general quaternion linear systemsquaternion Arnoldi methodquaternion generalized minimal residual methodquaternion Krylov subspacethree-dimensional signal filtering

Mathematics Subject Classification ID

Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Iterative numerical methods for linear systems (65F10)

Related Items (18)

Randomized quaternion QLP decomposition for low-rank approximation ⋮ Two algebraic methods for least squares L-structured and generalized L-structured problems of the commutative quaternion Stein matrix equation ⋮ Randomized Quaternion Singular Value Decomposition for Low-Rank Matrix Approximation ⋮ Computing partial quaternion eigenpairs with quaternion shift ⋮ Accuracy and stability of quaternion Gaussian elimination ⋮ Eigenvalues of quaternion tensors with applications to color video processing ⋮ On singular value decomposition and generalized inverse of a commutative quaternion matrix and applications ⋮ Harmonic multi-symplectic Lanczos algorithm for quaternion singular triplets ⋮ Block-row and block-column iterative algorithms for solving linear matrix equation ⋮ Semi‐tensor product of quaternion matrices and its application ⋮ Structure Preserving Quaternion Biconjugate Gradient Method ⋮ Quasi non-negative quaternion matrix factorization with application to color face recognition ⋮ Spherical Image Inpainting with Frame Transformation and Data-Driven Prior Deep Networks ⋮ New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems ⋮ On fast greedy block Kaczmarz methods for solving large consistent linear systems ⋮ GMRES algorithms over 35 years ⋮ The implicitly restarted multi-symplectic block-Lanczos method for large-scale Hermitian quaternion matrix eigenvalue problem and applications ⋮ A real structure-preserving algorithm based on the quaternion QR decomposition for the quaternion equality constrained least squares problem

Uses Software

• CGS

Cites Work

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• A new real structure-preserving quaternion QR algorithm
• A new structure-preserving method for quaternion Hermitian eigenvalue problems
• Lanczos method for large-scale quaternion singular value decomposition
• Block Krylov subspace methods for functions of matrices
• CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes
• Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES
• Robust quaternion matrix completion with applications to image inpainting
• Quaternions and matrices of quaternions
• Color Image Restoration by Saturation-Value Total Variation

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