Method illustrated in Chapter Eight of a Chinese text, The Nine Chapters on the Mathematical Art, that was written roughly two thousand years ago. Rediscovered in Europe by Isaac Newton (England) and Michel Rolle (France). Gauss called the method eliminiationem vulgarem (“common elimination”). Gauss adapted the method for another problem and developed notation.
As the computation use floating-point numbers, the Gaussian elimination method got the wrong answer due to round-off error.
These problems can be mitigated by choosing the pivot element carefully:
- Partial pivoting: Among rows with non-zero entries in column c, choose row with entry having largest absolute value.
- Complete pivoting: Instead of selecting order of columns beforehand, in each iteration choose column to maximize absolute value of pivot element.