论文信息 - Perturbation of parallel asynchronous linear iterations by floating point errors.

Perturbation of parallel asynchronous linear iterations by floating point errors.

This paper deals with parallel asynchronous linear iterations perturbed by errors in floating point arithmetic. An original result is presented which permits one to localize the limits of perturbed parallel asynchronous linear iterations. The result is established by using the approximate contraction concept. Simple examples are studied.

[1] Françoise Chaitin-Chatelin,et al. Lectures on finite precision computations , 1996, Software, environments, tools.

[2] John N. Tsitsiklis,et al. Parallel and distributed computation , 1989 .

[3] S. Gratton,et al. Convergence in finite precision of successive iteration methods under high nonnormality , 1996 .

[4] M. Tarazi. Some convergence results for asynchronous algorithms , 1982 .

[5] D. Szyld,et al. On asynchronous iterations , 2000 .

[6] Richard S. Varga,et al. Matrix Iterative Analysis , 2000, The Mathematical Gazette.

[7] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[8] Gérard M. Baudet,et al. Asynchronous Iterative Methods for Multiprocessors , 1978, JACM.

[9] J. Gillis,et al. Matrix Iterative Analysis , 1961 .

[10] M. A. Krasnoselʹskii,et al. Approximate Solution of Operator Equations , 1972 .

[11] Nicholas J. Higham,et al. INVERSE PROBLEMS NEWSLETTER , 1991 .

[12] James Hardy Wilkinson,et al. Rounding errors in algebraic processes , 1964, IFIP Congress.

[13] H. H. Schaefer. Banach Lattices and Positive Operators , 1975 .

[14] Paul Van Dooren,et al. Numerical analysis 2000 - Vol. III: Linear algebra , 2000 .

[15] D. Szyld,et al. ASYNCHRONOUS WEIGHTED ADDITIVE SCHWARZ METHODS , 1997 .