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Could anyone please evaluate my writing? The first paragram is as following:

-Begin-

The inverse analysis of an impact-force has presented researchers with a
dilemma. The analysis is extremely useful because it allows us to inversely es-
timate the pulse-type impact-force, which is difficult to be measured directly.
Unfortunately, the problem of inversely determining the pulse-type impact-force is ill-posed in sense of Hadamard's criteria . The solution method for
the problem is diffcult; its computational cost is high; and most important
of all, an accurate solution can hardly be obtained. The difficulty arises from
to the ill-posed nature of the governing equation; thus, some sort of numeri-
cal stabilization or regularization is necessary to produce a computable and
acceptable solution . The computational cost is relatively high by an order
or more because many solutions for various degrees of regularization have to
be calculated from which an optimal solution can be selected according to
certain objective function. Commonly, the objective function is a combina-
tion of a residual term and an error term. The accurate solution is also hard
to find because the governing equation of the ill-posed problem tends to in-
crease errors contained in data by several folds depending on the severity of
the problem. In a linear inverse problem, for an example, the perturbation
analysis has shown that the error in the data propagates into the solution
proportional with the magnitude of the condition number of the problem ;
therefore, for the present problems that have condition number in order of
105, an extremely small error in the data can easily produce an erroneous
solution without a proper regulation.
-End

The first paragraph is a bit long. I really thank you for your advise; it will definitely help me to improve my language skill. Thank you.
Upa
Hi,

This is not my area of technical expertise, but I'll do my best to offer some edits for the English.

The inverse analysis of an impact-force has presented researchers with a dilemma. This analysis wil be extremely useful because it allows us to inversely estimate the pulse-type impact-force, which is difficult to measure directly.Unfortunately, the problem of inversely determining the pulse-type impact-force is ill-posed in terms of Hadamard's criteria . The method of solving the problem is diffcult, its computational cost is high, and most important of all it will not really give accurate results. The difficulty arises from the ill-posed nature of the governing equation. Thus, some sort of numerical stabilization or regularization is necessary to produce a computable and acceptable solution . The computational cost is relatively high by one or more orders because many solutions for various degrees of regularization have to be calculated, from which an optimal solution can be selected according to a specific objective function. Commonly, the objective function is a combination of a residual term and an error term. An accurate solution is also hard to find because the governing equation of the ill-posed problem tends to increase errors contained in the data by several-folds, depending on the severity of the problem. In a linear inverse problem, for example, perturbation analysis has shown that the error in the data propagates into the solution proportional to the magnitude of the condition number of the problem . Therefore, for the present problems that have a condition number in order of 105, an extremely small error in the data can easily produce an erroneous
solution without proper regulation.

Clive
Students: Are you brave enough to let our tutors analyse your pronunciation?
Hi Clive,
Thank you so much for your time, effort, and input. However, could you please explain to me your revision particularly in the following aspects:

In the sentence: "An accurate solution is also hard to find because the governing equation of the ill-posed problem tends to increase errors contained in the data by several-folds.", why did you chose to use hyphen in 'several-folds'?

The second question is: On my last sentence, I used the article a: "a proper regularization", and you suggested to remove it. Could you please explain why?

Thank you so much.
Hi,
Thank you so much for your time, effort, and input. However, could you please explain to me your revision particularly in the following aspects:

In the sentence: "An accurate solution is also hard to find because the governing equation of the ill-posed problem tends to increase errors contained in the data by several-folds.", why did you chose to use hyphen in 'several-folds'?
We normally use the hyphenated suffix -fold with cardinal numbers, eg three-fold, five-fold.
I wouldn't use it with 'several'' myself. However, I decided it was OK but that it should follow the normal pattern for the suffix, ie include a hyphen.

The second question is: On my last sentence, I used the article a: "a proper regularization", and you suggested to remove it. Could you please explain why? I felt the phrase was used in a very general and 'uncountable' way.

Clive