The maximum count of arithmetic operations required for Gaussian elimination and Gauss-Jordan elimination is approximately 2n³ / 3, with a complexity of O(n³). Specifically, Gaussian elimination involves n(n+1) / 2 divisions, (2n³ + 3n² − 5n) / 6 multiplications, and (2n³ + 3n² − 5n) / 6 subtractions. The exponential growth of intermediate entries leads to exponential bit complexity, which is crucial for understanding the efficiency of these algorithms.
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but I don't understand how to get to this result.Gaussian elimination to solve a system of n equations for n unknowns requires n(n+1) / 2 divisions, (2n3 + 3n2 − 5n)/6 multiplications, and (2n3 + 3n2 − 5n)/6 subtractions,[4] for a total of approximately 2n3 / 3 operations. Thus it has arithmetic complexity of O(n3). However, the intermediate entries can grow exponentially large, so it has exponential bit complexity.