Teruyoshi Washizawa

Teruyoshi Washizawa, Akira Asai, Nobuhiro Yoshikawa

In topology optimization, the design parameter with no contribution to the objective function vanishes. This causes the stiffness matrix to become singular. We show that a local optimal solution is obtained by Conjugate Residual Method and Conjugate Gradient Method even if the stiffness matrix becomes singular. We prove that CGMconverges to a local optimal solution in that case. Computer simulation shows that CGM gives the same solutions obtained by CRM in case of a cantilever beam problem.

Yuichiro Miki, Teruyoshi Washizawa

The ILU-based preconditioning methods in previous work have their own parameters to improve their performances. Although the parameters may degrade the performance, their determination is left to users. Thus, these previous methods are not reliable in practical computer-aided engineering use. This paper proposes a novel ILU-based preconditioner called the auto-accelerated ILU, or A2ILU. In order to improve the convergence, A2ILU introduces acceleration parameters which modify the ILU factorized preconditioning matrix. A$^2$ILU needs no more operations than the original ILU because the acceleration parameters are optimized automatically by A2ILU itself. Numerical tests reveal the performance of A2ILU is superior to previous ILU-based methods with manually optimized parameters. The numerical tests also demonstrate the ability to apply auto-acceleration to ILU-based methods to improve their performances and robustness of parameter sensitivities.

Teruyoshi Washizawa

In conjugate gradient method, it is well known that the recursively computed residual differs from true one as the iteration proceeds in finite arithmetic. Some work have been devoted to analyze this be-havior and to evaluate the lower and the upper bounds of the difference. This paper focuses on the behavior of these two kinds of residuals, especially their lower bounds caused by the loss of trailing digit, respectively.

Teruyoshi Washizawa

Human eye movement mechanisms (saccades) are very useful for scene analysis, including object representation and pattern recognition. In this letter, a Hopfield neural network to emulate saccades is proposed. The network uses an energy function that includes location and identification tasks. Computer simulation shows that the network performs those tasks cooperatively. The result suggests that the network is applicable to shift-invariant pattern recognition.