The best replacement for gauss seidel is jacobi.

The best alternatives to gauss seidel are rated as following:
★★★★★  jacobi
★★★  newton raphson
★  conjugate gradient
★  sor

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Speaking about gauss seidel, one probably shouldn't forget about sor.

Other search terms related to gauss seidel and their ratings are:
★★★★★ sor
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