In this paper the authors describe a novel terminal attractor algorithm for solving linear systems, named ELISA. The method here presented is based on a special neural network continuous form of gradient descent, approaching the minimum of a quadratic function in a constant time, depending solely on the initial value of the residual function. The algorithm is founded on a new concept, called non-suspiciousness, which can be seen as a generalisation of convexity. Under general hypotheses it is proven that ELISA has a quadratic computational complexity and therefore is theoretically optimal. The preliminary numerical experiences clearly assess ELISA's efficiency both by dominant operation counting and in terms of CPU-time.

Bianchini, M., S., F., Gori, M., M., P. (1997). Solving Linear Systems by a Neural Network Canonical Form of Efficient Gradient Descent. In Proceedings of ICONIP‘97-ANZIIS‘97-ANNES‘97, Progress in Connectionist-Based Information Systems (pp.531-534). Singapore : Springer-Verlag.

Solving Linear Systems by a Neural Network Canonical Form of Efficient Gradient Descent

BIANCHINI, MONICA;GORI, MARCO;
1997-01-01

Abstract

In this paper the authors describe a novel terminal attractor algorithm for solving linear systems, named ELISA. The method here presented is based on a special neural network continuous form of gradient descent, approaching the minimum of a quadratic function in a constant time, depending solely on the initial value of the residual function. The algorithm is founded on a new concept, called non-suspiciousness, which can be seen as a generalisation of convexity. Under general hypotheses it is proven that ELISA has a quadratic computational complexity and therefore is theoretically optimal. The preliminary numerical experiences clearly assess ELISA's efficiency both by dominant operation counting and in terms of CPU-time.
1997
9813083611
Bianchini, M., S., F., Gori, M., M., P. (1997). Solving Linear Systems by a Neural Network Canonical Form of Efficient Gradient Descent. In Proceedings of ICONIP‘97-ANZIIS‘97-ANNES‘97, Progress in Connectionist-Based Information Systems (pp.531-534). Singapore : Springer-Verlag.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/28639
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