Newton`s iteration for inversion of Cauchy-like and other structured matrices

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:433341

Pan, V Y ^[1]; Zheng, Ailong; Huang, Xiaohan; Dias, O ^[2]

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1. Lehman College, Bronx, NY (United States)
2. CUNY, New York, NY (United States)

We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.

• Research Organization: Front Range Scientific Computations, Inc., Lakewood, CO (United States)
• OSTI ID: 433341
• Report Number(s): CONF-9604167--Vol.1; ON: DE96015306
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CAUCHY PROBLEM
COMPUTER CALCULATIONS
EFFICIENCY
ITERATIVE METHODS