different initial points

USAGE SUMMARY

The phrase "different initial points" is correct and usable in written English.
It can be used when discussing varying starting locations, perspectives, or conditions in a particular context. Example: "In our analysis, we considered different initial points to understand how they affect the outcome of the experiment."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

35 human-written examples

The evaluation consists of preparation of 400 tours with different initial points, start time, and tour durations.

Expert Systems with Applications

The results also indicate that the computational cost of the optimization process grows slowly with the number of the design variables, and the repeatability of the algorithm is very good when starting the search from different initial points.

Aerospace Science and Technology

different initial points with five cells.

EURASIP Journal on Wireless Communications and Networking

We executed this problem 10 times from different initial points.

Journal of Inequalities and Applications

Table 2 lists the numerical results of Problem 2 with different initial points.

Journal of Inequalities and Applications

We examine the behavior of the above iterations for the different initial points (see Table 1).

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

25 human-written examples

Note the different initial point of the firing threshold.

Nature

This results in the selection of a different initial point.

EURASIP Journal on Wireless Communications and Networking

One effective algorithm to increase the reliability is performing hillclimbing iteratively, each time with a different initial point, and then keeping the best solution.

BioMed Research International

Different initial-point thresholds are determined and given to areas with drastic and smooth changes in gray-level values.

EURASIP Journal on Image and Video Processing

We then generate at least 20 samples, each taken from the end of a single Markov chain initialized from different random initial points in the state space.

eLife

Expert writing Tips

Best practice

When describing simulations or optimization processes, clarify the method used to generate the "different initial points", such as random sampling or grid-based selection, to enhance reproducibility.

Common error

Avoid the assumption that using "different initial points" will always lead to finding the globally optimal solution. While it increases the chances, local optima may still trap the process. Consider employing global optimization techniques in conjunction.

Linguistic Context

The phrase "different initial points" typically functions as an adjectival phrase modifying a noun. It describes the varying origins or starting positions in a process, simulation, or analysis. As Ludwig AI explains, this phrase is usable and grammatically correct.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

The phrase "different initial points" is grammatically correct and commonly used, particularly in scientific and technical writing. According to Ludwig AI, the phrase is perfectly acceptable and serves to describe the varying origins or starting positions in processes such as simulations or optimization algorithms. To enhance clarity, specify the method for generating these points. Be cautious not to assume that using "different initial points" guarantees finding the global optimum; local optima can still pose a challenge. Consider using alternatives like ""varied starting points"" or ""multiple initial states"" to add variety to your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

varied starting points

Replaces "initial" with "starting" and "different" with "varied", emphasizing the diversity of origins.

diverse starting positions

Uses "positions" instead of "points" and "diverse" instead of "different", highlighting the variety of locations.

multiple initial states

Employs "states" instead of "points", suitable for contexts where conditions or stages are being described.

alternative initial locations

Substitutes "points" with "locations" and "different" with "alternative", focusing on the spatial aspect.

various initial coordinates

Replaces "points" with "coordinates", specifically useful in mathematical or geographical contexts.

distinct initial settings

Uses "settings" instead of "points", applicable when referring to the configuration at the beginning of a process.

varied initial conditions

Employs "conditions" instead of "points", highlighting the varying circumstances at the start.

divergent starting positions

Substitutes "different" with "divergent" and "points" with "positions", suggesting a branching out from various origins.

contrasting initial values

Replaces "points" with "values" and "different" with "contrasting", emphasizing the numerical aspect of the starting positions.

dissimilar initial spots

Uses "spots" instead of "points" and "dissimilar" instead of "different", focusing on the uniqueness of the locations.

FAQs

How can I use "different initial points" in a sentence?

You might say, "The algorithm was tested using "varied starting points" to ensure robustness" or "We explored the solution space by starting from "multiple initial states"".

What does "different initial points" mean in optimization?

In optimization, "different initial points" refers to starting an optimization algorithm from several distinct locations in the search space. This helps to avoid getting stuck in local optima and increases the likelihood of finding a global optimum.

Is there a difference between "different initial points" and "different starting points"?

The phrases "different initial points" and "different starting points" are largely interchangeable. The choice often depends on stylistic preference and the specific context.

Why use "different initial points" in simulations?

Using "different initial points" in simulations helps assess the sensitivity of the results to initial conditions. It also aids in exploring the range of possible outcomes and identifying potential instabilities or bifurcations.