the same solution as

USAGE SUMMARY

The phrase "the same solution as" is correct and usable in written English.
You can use it when comparing two solutions to indicate that they yield identical results or outcomes. Example: "After reviewing both methods, I found that they provide the same solution as the original approach."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The new approach found the same solution as much as 81% faster than the simple genetic algorithm and 9 53% faster than other previously formulated multiscale strategies.

Advances in Water Resources

It is the same solution as the Taylor theorem gives.

Harvard University

We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms.

Neural Networks

The algorithm is based on an alternative formulation of the structural SVM training problem that has the same solution as the conventional formulation.

Cornell University

The approach leads to exactly the same solution as found through lifted ILC, but at a much smaller computational load (O(N) vs O N3)) for both linear time-invariant (LTI) and linear time-varying (LTV) systems.

Mechatronics

We analyze the 'splitting errors' associated with the compositional SFI scheme, and we show how to control these errors in order to converge to the same solution as the Fully Implicit (FI) method.

Journal of Computational Physics

We develop a dynamic programming recursion for the solution of the equivalent perfect information problem, proving that the recursion is valid, an optimal solution exists, and results in the same solution as to the original problem.

Automatica

The key idea of ASPIN is to find the solution of the original system by solving a nonlinearly preconditioned system that has the same solution as the original system, but with more balanced nonlinearities.

Journal of Computational Physics

We show that the centralized OPF algorithm converges to a local minimum of the global OPF problem and that the distributed version of the algorithm converges to the same solution as the centralized one.

Electric Power Systems Research

Several test cases of plasmas enclosed by dielectrics and of glow discharges between electrodes show that the proposed equations yield the same solution as the standard equations but require 10 to 100 times fewer iterations to reach convergence whenever a quasi-neutral region forms.

Journal of Computational Physics

Mary: Are you solving the same problem with the same solution as when you started the company?

Forbes

Expert writing Tips

Best practice

When comparing different methods or approaches, use "the same solution as" to highlight that they ultimately lead to identical outcomes. This emphasizes the equivalence of their effectiveness, even if the processes differ.

Common error

Avoid using "the same solution as" when the results are only similar but not truly identical. Overstating the equivalence can mislead readers about the actual differences between the approaches.

Linguistic Context

The phrase "the same solution as" functions as a comparative conjunction, linking two different approaches, methods, or systems that ultimately yield an identical outcome. Ludwig AI confirms its wide applicability across diverse contexts.

Expression frequency: Very common

Frequent in

Science

75%

Academia

15%

News & Media

10%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "the same solution as" is a commonly used and grammatically correct phrase that functions as a comparative conjunction to indicate that different approaches or methods result in identical outcomes. According to Ludwig, this phrase is most frequently found in scientific, academic, and news media contexts. When using this phrase, be sure to highlight a true equivalence between solutions, avoiding overstatements. More formal alternatives include "an equivalent solution to" or "the identical solution to". Ludwig AI's analysis confirms the versatility and reliability of this phrase in various forms of writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the identical solution to

Emphasizes that the solution is exactly the same, highlighting the lack of any difference.

the very same solution as

Adds emphasis to the sameness of the solution, stressing that it's not just similar, but the exact same one.

an equivalent solution to

Focuses on the solution being functionally identical, differing slightly in emphasis from sharing the same solution.

an interchangeable solution with

Suggests that the solutions can be used in place of each other without affecting the outcome.

the same result as

Shifts the focus from the solution process to the outcome achieved.

a similar solution to

Indicates the solution is alike but not necessarily identical in every aspect.

a parallel solution to

Implies the solutions run alongside each other, offering a different perspective while achieving a similar end.

the analogous solution to

Highlights a similarity in function or appearance, indicating a parallel approach.

the equivalent approach to

Focuses on the method or strategy being equal, rather than the explicit solution.

a corresponding solution to

Suggests that the solutions are related or linked, implying a connection between them.

FAQs

How can I rephrase "the same solution as" to sound more formal?

For a more formal tone, consider using phrases like "an "equivalent solution to"" or "the "identical solution to"". These alternatives maintain the meaning while elevating the formality.

When is it appropriate to use "the same solution as" in scientific writing?

Use "the same solution as" in scientific writing when comparing different methods or algorithms that converge to the exact same result. This clarifies that despite potential differences in process, the final outcome is identical.

What's the difference between "a similar solution to" and "the same solution as"?

"A "similar solution to"" implies the outcomes are alike but not necessarily identical. "The same solution as" indicates that the results are exactly the same, leaving no room for variation.

Is it redundant to say "exactly the same solution as"?

While not strictly redundant, adding "exactly" to "the same solution as" can add emphasis. However, "the same" already implies no difference, so "exactly the same solution as" might be seen as slightly verbose in some contexts.