iterative method

USAGE SUMMARY

The phrase "iterative method" is an appropriate and usable phrase in written English.
It is often used to describe a problem-solving approach in which repeated calculations or approximations are made until a desired result is achieved. For example, an iterative method could be used to find the roots of a polynomial equation.

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Table 1 Numbers of iterations for the Newton iterative method.

Boundary Value Problems

We see that the iterative method converges within seven iterations.

Advances in Difference Equations

Such an iterative method is known as Ishikawa iteration.

Journal of Inequalities and Applications

Such an iterative method is known as Noor iteration.

Journal of Inequalities and Applications

Newton iterative method is used.

Journal of Computational Physics

The effect of variation in C i on R d was corrected using the iterative method of Kirschbaum and Farquhar47.

Nature

Nurhuda, M. & Faisal, F. H. Numerical solution of time-dependent Schrödinger equation for multiphoton processes: a matrix iterative method.

Nature

By a new technique, strong uniqueness conditions for both Stokes type iterative method (Iterative method I) and Newton iterative method (Iterative method II) are obtained, which are weaker than the ones reported in open literature.

Computer Methods in Applied Mechanics and Engineering

A fourth-order iterative method for quadratic equations is presented.

Journal of Computational and Applied Mathematics

Some examples are solved using the proposed iterative method.

Signal Processing

Furthermore, we introduce an iterative method to improve the quality.

Information Sciences

Expert writing Tips

Best practice

When describing an "iterative method", clearly state the convergence criteria and the stopping condition to ensure reproducibility and avoid infinite loops.

Common error

Avoid vague descriptions of the "iterative method". Always specify the exact calculations performed in each iteration, and how the results from one iteration influence the next.

Linguistic Context

The phrase "iterative method" functions as a noun phrase, typically used as a subject or object in a sentence. According to Ludwig AI, this phrase is perfectly acceptable in written English, often used to describe problem-solving approaches.

Expression frequency: Very common

Frequent in

Science

95%

Academia

3%

Formal & Business

1%

Less common in

News & Media

0.5%

Encyclopedias

0.3%

Wiki

0.2%

Ludwig's WRAP-UP

The phrase "iterative method" is a common and grammatically correct term, predominantly used in scientific and academic writing to describe problem-solving techniques involving repetitive steps. Ludwig AI confirms the phrase's appropriateness and usability. When employing this phrase, ensure you provide a clear explanation of each iteration step and specify the conditions for convergence. Alternatives include "repetitive process" and "successive approximation", but "iterative method" is the most precise and widely recognized term in technical contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

iterative algorithm

Replaces 'method' with 'algorithm', common in computer science.

iterative solution

Focuses on the outcome achieved through iteration.

repetitive process

Replaces 'method' with 'process' to emphasize the sequential nature.

successive approximation

Highlights the incremental approach towards a solution.

recursive technique

Emphasizes the self-referential nature of the method.

step-by-step approach

Focuses on the gradual progression towards a result.

incremental procedure

Stresses the progressive refinement of the solution.

cyclic algorithm

Emphasizes the repeating nature of the algorithm.

repeated calculation

Highlights the computational aspect of the process.

trial-and-error process

Emphasizes the experimental nature of the method.

FAQs

How is an "iterative method" used in problem-solving?

An "iterative method" involves repeating a process or calculation multiple times, each time refining the result, until a desired level of accuracy or convergence is achieved. It's used when a direct solution is difficult or impossible to obtain.

What's the difference between an "iterative method" and a direct method?

An "iterative method" approximates a solution through successive steps, while a direct method solves a problem in a finite number of steps, providing an exact solution (assuming no numerical errors). The choice depends on the problem's complexity and required accuracy.

What are some examples of "iterative methods" in mathematics?

Examples include Newton's method for finding roots of equations, gradient descent for optimization problems, and the Jacobi method for solving linear systems. Each involves repeated calculations to get closer to the solution.

What are some alternatives to using an "iterative method"?

Alternatives depend on the specific problem, but might include analytical solutions (if possible), approximation techniques like perturbation theory, or using different numerical methods altogether. For semantically related alternatives, you can consider phrases like "repetitive process" or "successive approximation".