Optimal Asynchronous Newton Method for the Solution of Nonlinear Equations
Journal of the ACM (JACM)
Adaptive signal processing
VLSI array processors
Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
A fully parallel algorithm for the symmetric eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Artificial neural networks: electronic implementations
Artificial neural networks: electronic implementations
Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Parallel structured networks for solving a wide variety of matrix algebra problems
Journal of Parallel and Distributed Computing - Special issue on neural computing on massively parallel processing
On Stable Parallel Linear System Solvers
Journal of the ACM (JACM)
Solving Linear Algebraic Equations on an MIMD Computer
Journal of the ACM (JACM)
Optimization by Vector Space Methods
Optimization by Vector Space Methods
VLSI Design of Neural Networks
VLSI Design of Neural Networks
VLSI Systems and Computations
A Divide and Conquer Algorithm for Computing the Singular Value Decomposition
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
A Novel Approach Solving for Linear Matrix Inequalities UsingNeural Networks
Neural Processing Letters
Matrix Manipulations Using Artificial Neural Networks
Journal of Integrated Design & Process Science
IEEE Transactions on Fuzzy Systems
Structured neural networks for constrained model predictive control
Automatica (Journal of IFAC)
Recurrent neural networks for nonlinear output regulation
Automatica (Journal of IFAC)
A recurrent neural network for computing pseudoinverse matrices
Mathematical and Computer Modelling: An International Journal
Recurrent neural networks for LU decomposition and Cholesky factorization
Mathematical and Computer Modelling: An International Journal
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Two three-dimensional structured networks are developed for solving linear equations and the Lyapunov equation. The basic idea of the structured network approaches is to first represent a given equation-solving problem by a 3-D structured network so that if the network matches a desired pattern array, the weights of the linear neurons give the solution to the problem: then, train the 3-D structured network to match the desired pattern array using some training algorithms; and finally, obtain the solution to the specific problem from the converged weights of the network. The training algorithms for the two 3-D structured networks are proved to converge exponentially fast to the correct solutions. Simulations were performed to show the detailed convergence behaviors of the 3-D structured networks.