linearizing

简明释义

英[ˈlɪniəraɪzɪŋ]美[ˈlɪnɪəraɪzɪŋ]

adj. 线性化；线性的

v. 使线性化（linearize 的 ing 形式）；以线表示

英英释义

单词用法

同义词

反义词

例句

1.The principle of linearizing VCO by reactance compensation is discussed. The design of the practical VCO is given.

文中讨论了使V CO线性化的电抗补偿原理并给出了用多节电抗网络补偿的VCO设计实例。

2.First locally linearizing nonlinear system at equilibrium to investigate show stability of system, obtain some practicability conclusions and formulas.

首先，通过对系统线性化方程的特征方程根的分布分析，给出了滞量对系统稳定性影响的具体结论和公式。

3.The uniqueness of the nicely nonlinear model and its linearizing compensator is proved under some constraints.

针对良好非线性模型及其线性化补偿器问题，证明两者在一定约束条件下存在的惟一性。

4.A linearizing and decoupling scheme is provided and made the system linearized and decoupled.

提出一种可使该系统实现线性化和部分解耦的方案。

5.For easy application, a new robust filter, which is the extended linearizing realization of the solution, is provided.

并对该解进行扩展线性化处理，得到了一个较易实现的扩展鲁棒滤波算法。

6.To study vibration systems or the multibody systems with small displacements efficiently, a computerized algebraic method for linearizing the equations of multibody system is discussed in this paper.

为研究多体系统小位移或振动问题，从多体系统动力学方程出发，讨论微分-代数方程线性化计算机代数问题。

7.The swing equation of gyro theodolite is nonlinearity, and data processing result is not good after linearizing.

陀螺的摆动方程是非线性的，线性化后的数据处理结果都不理想。

8.With the premise of linearizing for the signal process, an equation for the angular resolution of the scanning laser radar is recommended according to the Rayleigh′s criterion for the intensity image.

在信号过程线性的前提下，根据强度象的瑞利判据建议扫描激光雷达角分辨本领公式。

9.In machine learning, we often use techniques for linearizing 线性化 complex data relationships to improve model accuracy.

在机器学习中，我们经常使用技术来线性化复杂的数据关系，以提高模型的准确性。

10.The engineer suggested linearizing 线性化 the system's response curve to simplify the analysis.

工程师建议线性化系统的响应曲线，以简化分析。

11.By linearizing 线性化 the equations, we can solve them more easily using standard methods.

通过线性化方程，我们可以更容易地使用标准方法求解它们。

12.In control theory, linearizing 线性化 a nonlinear system helps in designing effective controllers.

在控制理论中，线性化非线性系统有助于设计有效的控制器。

13.The researcher focused on linearizing 线性化 the data to identify trends more clearly.

研究人员专注于线性化数据，以更清晰地识别趋势。

作文

In the realm of mathematics and engineering, the concept of linearizing (线性化) plays a crucial role in simplifying complex systems. Often, real-world phenomena are described by nonlinear equations, which can be challenging to analyze and solve. By applying the process of linearizing (线性化), we transform these nonlinear relationships into linear ones, making them much more manageable. This technique is particularly useful in fields such as control theory, where engineers need to predict system behavior accurately.To understand linearizing (线性化), let’s consider an example from physics. Imagine a pendulum swinging back and forth. The motion of the pendulum can be described by a nonlinear differential equation. However, if we only consider small angles of swing, we can approximate this motion using a linear equation. This approximation simplifies our calculations and allows us to apply linear algebra techniques to analyze the system.The process of linearizing (线性化) typically involves taking the first derivative of a function at a specific point, known as the point of linearization. This derivative provides the slope of the tangent line at that point, which serves as the linear approximation of the function. For instance, in the case of our pendulum, we would evaluate the angle and its rate of change at the equilibrium position to derive a linear model that describes its behavior near that point.Another important aspect of linearizing (线性化) is its application in optimization problems. Many optimization algorithms rely on linear approximations to find the best solution efficiently. By linearizing (线性化) the objective function and constraints, we can utilize linear programming techniques to arrive at solutions that are computationally feasible. This approach is particularly beneficial in operations research, where decision-makers often face complex logistical challenges.However, it is essential to recognize the limitations of linearizing (线性化). While this technique can simplify analysis, it may also introduce errors, especially when applied outside the valid range of linear approximation. For example, if we attempt to use a linear model to predict the behavior of a highly nonlinear system across a wide range of inputs, we may encounter significant discrepancies between the predicted and actual outcomes. Therefore, understanding the context and scope of linearizing (线性化) is vital for effective application.In conclusion, linearizing (线性化) is a powerful mathematical tool that enables us to simplify complex nonlinear relationships into more manageable linear forms. Its applications span various fields, including physics, engineering, and optimization. While it offers numerous advantages, practitioners must remain aware of its limitations and ensure that they apply it within appropriate contexts. By mastering the art of linearizing (线性化), we can enhance our analytical capabilities and tackle real-world challenges with greater confidence and precision.

在数学和工程的领域中，linearizing（线性化）这一概念在简化复杂系统方面发挥着至关重要的作用。现实世界的现象通常由非线性方程描述，这可能会让分析和求解变得具有挑战性。通过应用linearizing（线性化）过程，我们可以将这些非线性关系转化为线性关系，从而使它们变得更加易于处理。这一技术在控制理论等领域尤为有用，在这些领域中，工程师需要准确预测系统行为。为了理解linearizing（线性化），让我们考虑一个来自物理学的例子。想象一个摆动的摆。摆的运动可以用一个非线性微分方程来描述。然而，如果我们只考虑小角度的摆动，我们可以使用线性方程来近似这个运动。这种近似简化了我们的计算，并允许我们应用线性代数技术来分析该系统。linearizing（线性化）过程通常涉及在特定点取函数的一阶导数，该点称为线性化点。这个导数提供了该点切线的斜率，作为函数的线性近似。例如，在我们的摆的情况下，我们会在平衡位置评估角度及其变化率，以推导出描述其在该点附近行为的线性模型。linearizing（线性化）的另一个重要方面是其在优化问题中的应用。许多优化算法依赖于线性近似，以有效地找到最佳解决方案。通过linearizing（线性化）目标函数和约束条件，我们可以利用线性规划技术到达计算上可行的解决方案。这种方法在运筹学中尤其有益，因为决策者经常面临复杂的物流挑战。然而，必须认识到linearizing（线性化）的局限性。虽然这一技术可以简化分析，但在超出线性近似的有效范围时，可能会引入误差。例如，如果我们试图使用线性模型预测高度非线性系统在广泛输入下的行为，我们可能会遇到预测结果与实际结果之间的显著差异。因此，理解linearizing（线性化）的背景和范围对有效应用至关重要。总之，linearizing（线性化）是一个强大的数学工具，使我们能够将复杂的非线性关系简化为更易于处理的线性形式。它的应用跨越多个领域，包括物理学、工程学和优化。虽然它提供了许多优势，但从业者必须保持对其局限性的意识，并确保在适当的背景下应用它。通过掌握linearizing（线性化）的艺术，我们可以增强我们的分析能力，更加自信和精确地应对现实世界的挑战。