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    Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations
    (2022-01-01)
    Tansri, Kanjanaporn
    ;
    Choomklang, Sarawanee
    ;
    Chansangiam, Pattrawut
    We develop an effective algorithm to find a well-approximate solution of a generalized Sylvester-transpose matrix equation where all coefficient matrices and an unknown matrix are rectangular. The algorithm aims to construct a finite sequence of approximated solutions from any given initial matrix. It turns out that the associated residual matrices are orthogonal, and thus, the desire solution comes out in the final step with a satisfactory error. We provide numerical experiments to show the capability and performance of the algorithm.
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    Analytical incremental learning: Fast constructive learning method for neural network
    (2016-01-01)
    Alfarozi, Syukron Abu Ishaq
    ;
    Setiawan, Noor Akhmad
    ;
    Adji, Teguh Bharata
    ;
    Woraratpanya, Kuntpong
    ;
    Pasupa, Kitsuchart
    Extreme learning machine (ELM) is a fast learning algorithm for single hidden layer feed-forward neural network (SLFN) based on random input weights which usually requires large number of hidden nodes. Recently, novel constructive and destructive parsimonious (CP and DP)-ELM which provide the effectiveness generalization and compact hidden nodes have been proposed. However, the performance might be unstable due to the randomization either in ordinary ELM or CP and DP-ELM. In this study, analytical incremental learning (AIL) algorithm is proposed in which all weights of neural network are calculated analytically without any randomization. The hidden nodes of AIL are incrementally generated based on residual error using least square (LS) method. The results show the effectiveness of AIL which has not only smallest number of hidden nodes and more stable but also good generalization than those of ELM, CP and DP-ELM based on seven benchmark data sets evaluation.