Least squares solution with the minimum-norm to general matrix equations via iteration

DOI10.1016/j.amc.2009.10.052zbMath1186.65047OpenAlexW2046512631MaRDI QIDQ846468

N. E. Zubov

Publication date: 9 February 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.10.052

zbMATH Keywords

convergenceiterative algorithmLyapunov matrix equationminimal norm least squares solutionSylvester matrix equationoptimal step sizegeneral linear matrix equations

Mathematics Subject Classification ID

Related Items (21)

Parametric Solutions to the Generalized Discrete Yakubovich-Transpose Matrix Equation ⋮ Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations ⋮ New proof of the gradient-based iterative algorithm for the Sylvester conjugate matrix equation ⋮ Closed-form solutions to the nonhomogeneous Yakubovich-transpose matrix equation ⋮ Precision matrix estimation using penalized generalized Sylvester matrix equation ⋮ A finite iterative algorithm for solving the complex generalized coupled Sylvester matrix equations by using the linear operators ⋮ Uniqueness of solution of a generalized \(\star\)-Sylvester matrix equation ⋮ An efficient algorithm for solving extended Sylvester-conjugate transpose matrix equations ⋮ Iterative solutions to coupled Sylvester-transpose matrix equations ⋮ Gradient-based iterative algorithms for generalized coupled Sylvester-conjugate matrix equations ⋮ An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations ⋮ Reduced-rank gradient-based algorithms for generalized coupled Sylvester matrix equations and its applications ⋮ Positive operator based iterative algorithms for solving Lyapunov equations for Itô stochastic systems with Markovian jumps ⋮ Toward solution of matrix equation \(X=Af(X)B+C\) ⋮ Iterative solution to a system of matrix equations ⋮ Matrix equations over \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices ⋮ Finite iterative method for solving coupled Sylvester-transpose matrix equations ⋮ Iterative algorithm for solving a class of quaternion matrix equation over the generalized \((P, Q)\)-reflexive matrices ⋮ LSMR iterative method for general coupled matrix equations ⋮ The generalized QMRCGSTAB algorithm for solving Sylvester-transpose matrix equations ⋮ On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations

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