linearized

简明释义

英[ˈlɪnəraɪzd]美[ˈlɪnəˌraɪzd]

adj. 线性化的

英英释义

单词用法

同义词

反义词

例句

1.One of the algorithms is to linearized the state equation based on the optimal estimation.

其中一种方法是基于当前最优估计值对状态方程进行线性化。

2.The model was linearized for the qualitative analysis of the pneumatic system.

为便于进行定性分析，对该数学模型进行了线性化处理。

3.The other is the Linearized Optimization Layer by Layer (LOLL) algorithm which speeds up MLP's training procedure.

为了提高MLP的训练速度，提出了一种线性化逐层优化（LOLL） MLP训练算法。

4.A three-dimensional linearized elastodynamic inversion method to reconstruct the shape of scatterer has been investigated in this paper.

用三维线弹性动力学的反演方法重构了弹性介质中散射体的形状。

5.Established a linearized oscillation result of the second order nonlinear neutral delay differential equation with positive and negative coefficients.

建立了二阶具正负系数的非线性中立型微分方程的一个线性化振动性结果。

6.The nonlinear parabolic equation thus formed is linearized through proofread-correct method and is solved by LU decomposition.

应用预估校正法对所形成的非线性抛物型方程进行线性化，采用追赶法进行求解。

7.Acording to features of production hyperbolic decline equation, a linearized method of solving nonlinear hyperbolic decline equation is proposed out.

根据产量双曲递减方程的特点，提出了非线性双曲方程的线性化求解方法。

8.The data was linearized to simplify the analysis.

数据被线性化以简化分析。

9.By linearizing the system, we can better understand its behavior near equilibrium.

通过线性化系统，我们可以更好地理解其在平衡点附近的行为。

10.In order to apply regression techniques, we linearized the non-linear model.

为了应用回归技术，我们将非线性模型线性化。

11.The research paper discussed how the data was linearized for clarity.

研究论文讨论了数据是如何被线性化以提高清晰度的。

12.The engineer linearized the equations to make them easier to solve.

工程师将方程式线性化以便更容易求解。

作文

In the field of mathematics and engineering, the concept of linearization plays a crucial role in simplifying complex systems. When we encounter nonlinear equations or functions, it can be quite challenging to analyze their behavior. To make these problems more manageable, we often use a technique known as linearization, which involves approximating a nonlinear function by a linear one around a specific point. This process allows us to study the system's behavior in a simplified manner. In this context, the term linearized refers to the transformation of a nonlinear model into a linear form. For instance, consider a simple example of a pendulum swinging back and forth. The motion of the pendulum can be described by a nonlinear differential equation due to the sine function involved in its dynamics. However, if we are only interested in small angles, we can approximate the sine function by its Taylor series expansion, leading to a linear equation. This approximation is valid only near the equilibrium position, where the angle is small. Thus, we say that the pendulum's motion has been linearized for small angles. The benefits of linearized models are numerous. They allow engineers and scientists to use powerful mathematical tools from linear algebra, making it easier to analyze stability, control systems, and predict system behavior. For example, in control theory, a linearized model of a dynamic system can be used to design controllers that stabilize the system around an operating point. This approach is particularly useful in robotics, aerospace, and other fields where precision and reliability are paramount. However, it is essential to recognize the limitations of linearized models. Since they are based on approximations, they may not accurately represent the system's behavior over a wide range of inputs or conditions. As such, relying solely on a linearized model can lead to incorrect conclusions or designs if the system operates outside the range for which the linearization is valid. Therefore, while linearized models are invaluable tools, they should be used with caution and supplemented with more comprehensive analyses when necessary. In conclusion, the process of linearization serves as an essential technique in various scientific and engineering disciplines. By transforming complex nonlinear functions into simpler linear forms, we gain valuable insights into system behavior and can apply effective analytical tools. Nevertheless, understanding the limitations of linearized models is critical for ensuring accurate predictions and successful applications in real-world scenarios. As we continue to explore the intricacies of dynamic systems, the balance between simplification through linearization and the acknowledgment of their boundaries will remain a key aspect of our analytical toolkit.

在数学和工程领域，线性化的概念在简化复杂系统中发挥着至关重要的作用。当我们遇到非线性方程或函数时，分析其行为可能非常具有挑战性。为了使这些问题更易于处理，我们通常使用一种称为线性化的技术，该技术涉及在特定点附近用线性函数来近似非线性函数。这一过程使我们能够以简化的方式研究系统的行为。在这个背景下，术语linearized指的是将非线性模型转变为线性形式的过程。例如，考虑一个简单的摆动 pendulum 来回摆动的例子。摆动的运动可以通过非线性微分方程来描述，因为其动态中涉及正弦函数。然而，如果我们只对小角度感兴趣，我们可以通过泰勒级数展开来近似正弦函数，从而得到一个线性方程。这个近似仅在平衡位置附近有效，即角度较小时。因此，我们说摆动的运动已经被linearized，适用于小角度。Linearized模型的好处是显而易见的。它们允许工程师和科学家使用线性代数中的强大数学工具，从而更容易分析稳定性、控制系统并预测系统行为。例如，在控制理论中，动态系统的linearized模型可以用来设计在操作点附近稳定系统的控制器。这种方法在机器人、航空航天和其他对精度和可靠性要求极高的领域特别有用。然而，必须认识到linearized模型的局限性。由于它们基于近似，因此可能无法准确表示系统在广泛输入或条件下的行为。因此，仅依赖于linearized模型可能会导致错误的结论或设计，尤其是在系统在超出线性化有效范围的情况下。因此，尽管linearized模型是宝贵的工具，但在必要时应谨慎使用，并辅之以更全面的分析。总之，linearization过程在各个科学和工程学科中作为一种基本技术。通过将复杂的非线性函数转变为更简单的线性形式，我们获得了对系统行为的宝贵洞察，并能够应用有效的分析工具。然而，理解linearized模型的局限性对于确保准确的预测和成功的实际应用至关重要。在我们继续探索动态系统的复杂性时，通过linearization实现简化与承认其边界之间的平衡将始终是我们分析工具箱的关键方面。