TY - JOUR

T1 - Vector labelling method in fixed points algorithm and array processors

AU - Oishi, Shin'Ichi

AU - Takase, Tadaaki

AU - Yamamura, Kiyotaka

PY - 1983

Y1 - 1983

N2 - Studies of fixed point algorithms have advanced greatly in the last decade. These algorithms have been developed to construct globally fixed points of finite‐dimensional continuous maps, to which existence of fixed points is guaranteed by, for instance, Brouwer's fixed point theorem. However, it is pointed out that these algorithms become progressively slower with increasing dimension. In this paper it is shown that the vector labelling algorithm, one of the typical fixed point algorithms, can be performed efficiently in parallel on a suitable array processor system. Under certain conditions, the time complexity of the vector labelling algorithm is determined by pivot operations. It is shown that high parallel efficiency about 0.9 is attained by executing these pivot operations on our array processor. to further speed up the algorithm, a method is also shown for evading matrix inversion formerly needed at the beginning of the vector labelling algorithm.

AB - Studies of fixed point algorithms have advanced greatly in the last decade. These algorithms have been developed to construct globally fixed points of finite‐dimensional continuous maps, to which existence of fixed points is guaranteed by, for instance, Brouwer's fixed point theorem. However, it is pointed out that these algorithms become progressively slower with increasing dimension. In this paper it is shown that the vector labelling algorithm, one of the typical fixed point algorithms, can be performed efficiently in parallel on a suitable array processor system. Under certain conditions, the time complexity of the vector labelling algorithm is determined by pivot operations. It is shown that high parallel efficiency about 0.9 is attained by executing these pivot operations on our array processor. to further speed up the algorithm, a method is also shown for evading matrix inversion formerly needed at the beginning of the vector labelling algorithm.

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U2 - 10.1002/ecja.4400661108

DO - 10.1002/ecja.4400661108

M3 - Article

AN - SCOPUS:0020849743

VL - 66

SP - 51

EP - 59

JO - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 8756-6621

IS - 11

ER -