Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm
Copyright policy )Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm
AbstractThis paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.
Economics, Matrix (chemical analysis), generalized Sylvester-transpose matrix equation, Estimator, least-squares solution, Engineering, Differential equation, Eigenvalues and eigenvectors, Numerical Analysis, Numerical Optimization Techniques, Recursive Algorithms, Physics, Mathematical optimization, Statistics, Iterative method, Algorithm, Computational Theory and Mathematics, Numerical methods for matrix equations, Physical Sciences, Convergence (economics), Iterative Methods, Sum of Squares Techniques, Artificial neural network, Composite material, Convex Optimization, Mathematical analysis, Quantum mechanics, iterative method, Machine learning, Generalized Sylvester-transpose matrix equation, Least-squares solution, QA1-939, FOS: Mathematics, Genetics, Transpose, Biology, gradient descent, Economic growth, Matrix Algorithms and Iterative Methods, Gradient descent, Matrix equations and identities, Applied mathematics, System Identification Techniques, Computer science, Materials science, Control and Systems Engineering, FOS: Biological sciences, Computer Science, Mathematics, Least-squares function approximation, Ordinary differential equation, Matrix Computations, Sequence (biology)
Economics, Matrix (chemical analysis), generalized Sylvester-transpose matrix equation, Estimator, least-squares solution, Engineering, Differential equation, Eigenvalues and eigenvectors, Numerical Analysis, Numerical Optimization Techniques, Recursive Algorithms, Physics, Mathematical optimization, Statistics, Iterative method, Algorithm, Computational Theory and Mathematics, Numerical methods for matrix equations, Physical Sciences, Convergence (economics), Iterative Methods, Sum of Squares Techniques, Artificial neural network, Composite material, Convex Optimization, Mathematical analysis, Quantum mechanics, iterative method, Machine learning, Generalized Sylvester-transpose matrix equation, Least-squares solution, QA1-939, FOS: Mathematics, Genetics, Transpose, Biology, gradient descent, Economic growth, Matrix Algorithms and Iterative Methods, Gradient descent, Matrix equations and identities, Applied mathematics, System Identification Techniques, Computer science, Materials science, Control and Systems Engineering, FOS: Biological sciences, Computer Science, Mathematics, Least-squares function approximation, Ordinary differential equation, Matrix Computations, Sequence (biology)
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