Divergence

The failure of a numerical method or iterative process to approach the intended solution, often producing increasingly inaccurate results.

Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.

Divergence means the failure of a numerical method or iterative process to approach the intended solution, so instead of settling towards an answer the computation moves away from it. This failure often produces increasingly inaccurate results as the process continues. Divergence is therefore the opposite of the desired behaviour, in which successive steps draw closer to the solution Spotting divergence early lets a failing process be halted or replaced before its worsening figures are mistaken for a solution, which is why iterative computations are watched for this behaviour.

Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.

Divergence is signalled by results that grow increasingly inaccurate rather than settling towards a solution, since it is the failure of a numerical method or iterative process to approach the intended answer. Successive estimates may swing more widely or grow without bound instead of stabilising. This drift away from the intended solution is the visible sign that a process is diverging Spotting divergence early lets a failing process be halted or replaced before its worsening figures are mistaken for a solution, which is why iterative computations are watched for this behaviour.

Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.

Divergence is a problem because it is the failure of a numerical method or iterative process to approach the intended solution, so the computation yields no usable answer and often produces increasingly inaccurate results. Continuing a diverging process wastes effort and can give misleading figures. Recognising divergence lets a diverging method be stopped or replaced before its worsening results are mistaken for a solution Spotting divergence early lets a failing process be halted or replaced before its worsening figures are mistaken for a solution, which is why iterative computations are watched for this behaviour.

Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.

Divergence can occur in an iterative process, since it is defined as the failure of a numerical method or iterative process to approach the intended solution. When the repeated update pushes estimates away from the answer rather than towards it, the iteration diverges and its results grow increasingly inaccurate. This possibility is why an iterative process is monitored to check whether it is approaching or moving away from the solution Spotting divergence early lets a failing process be halted or replaced before its worsening figures are mistaken for a solution, which is why iterative computations are watched for this behaviour.

Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.

Divergence is the failure of a numerical method or iterative process to approach the intended solution, while convergence is the process by which successive approximations produced by a numerical method approach the true solution. The two are opposites, describing whether a process moves towards or away from the answer. A method is judged by whether it converges, and divergence marks the case where that desired approach fails Spotting divergence early lets a failing process be halted or replaced before its worsening figures are mistaken for a solution, which is why iterative computations are watched for this behaviour.

Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.