Note on dynamic relaxation

✍ Scribed by Winifred L. Wood

• Publisher: John Wiley and Sons
• Year: 1971
• Tongue: English
• Weight: 118 KB
• Volume: 3
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620030115

✦ Synopsis

The Dynamic Relaxation (DR) method of solving a set of simultaneous linear equations requires an estimate of the spectral radius of the matrix. Dividing each equation by the corresponding row sum of moduli of the elements of the matrix gives a convenient upper bound of unity to this. This note shows that the DR method then gives a faster asymptotic rate of the convergence than the degenerate Chebyshev method which it closely resembles.

We suppose the problem is to solve the system of simultaneous linear equations

A x = a

(1)