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Round-off error analysis of iterations for large linear systems (1978)

Woźniakowski, H.

Springer

Numerische Mathematik 30 (1978), S. 301-314

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ISSN: 0945-3245

Keywords: AMS(MOS): 65F10 ; CR: 5.14

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary We deal with the rounding error analysis of successive approximation iterations for the solution of large linear systemsA x =b. We prove that Jacobi, Richardson, Gauss-Seidel and SOR iterations arenumerically stable wheneverA=A *〉0 andA has PropertyA. This means that the computed resultx k approximates the exact solution α with relative error of order ζ ‖A‖·‖A −1‖ where ζ is the relative computer precision. However with the exception of Gauss-Seidel iteration the residual vector ‖Ax k −b‖ is of order ζ ‖A‖2 ‖A −1‖ ‖α‖ and hence the remaining three iterations arenot well-behaved.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01411845

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