relaxation method
Definition
Noun: A computational technique for solving a system of equations. It starts with an initial estimate (guess) for the solution. The method then iteratively refines this guess by systematically reducing the errors. This process of successive approximations continues until the errors fall below a pre-defined acceptable level.
Usage
The term is used primarily in mathematics, physics, and engineering contexts to describe a specific numerical algorithm. * The engineer used a relaxation method to find the voltage values at different nodes in the complex circuit. * For solving the large set of linear equations derived from the model, a relaxation method proved more efficient than a direct approach.
Advanced Usage
- Successive Over-Relaxation (SOR): This is a common variant of the basic relaxation method that uses a weighted average to accelerate convergence. It is a standard technique in computational fluid dynamics.
- Applying the Successive Over-Relaxation method significantly reduced the number of iterations needed to solve the matrix equation.
Variants and Related Words
- Relaxation (in this context): The iterative process of reducing error in an approximation.
- The relaxation of the initial guess converged to the correct solution after 50 cycles.
- Iterative Method: A broader category of algorithms that generate a sequence of improving approximate solutions, which includes relaxation methods.
Synonyms
- Iterative approximation technique
- Successive approximation method
Related Phrases
- To converge to a solution: This phrase describes the goal of the relaxation method.
- With a good initial guess, the relaxation algorithm will converge to a solution quickly.
- To iterate until convergence: Describes the core procedure of the method.
- The program was designed to iterate until convergence, using the specified error tolerance.
Noun
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a method of solving simultaneous equations by guessing a solution and then reducing the errors that result by successive approximations until all the errors are less than some specified amount
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