successive approximation

简明释义

逐次比较法

英英释义

例句

1.In numerical methods, successive approximation is often used to find roots of equations.

在数值方法中，逐次逼近通常用于寻找方程的根。

2.The algorithm employs successive approximation to refine the solution until it meets the desired accuracy.

该算法采用逐次逼近来精细化解决方案，直到达到所需的精度。

3.The teacher explained successive approximation as a method to gradually approach the correct answer.

老师解释了逐次逼近作为一种逐步接近正确答案的方法。

4.Engineers use successive approximation techniques in control systems to improve stability.

工程师在控制系统中使用逐次逼近技术来提高稳定性。

5.In machine learning, successive approximation can be applied to optimize model parameters.

在机器学习中，逐次逼近可以应用于优化模型参数。

作文

The concept of successive approximation is a vital principle in various fields, including mathematics, engineering, and psychology. It refers to the process of gradually approaching a desired outcome or target through incremental steps or adjustments. This method is particularly useful when dealing with complex problems where direct solutions are not readily available. By breaking down a problem into smaller, more manageable components, individuals can make steady progress towards their goals.In mathematics, successive approximation is often used in numerical methods to find solutions to equations that cannot be solved analytically. For instance, when trying to determine the roots of a polynomial, one might start with an initial guess and then refine that guess based on the function's behavior. Each iteration brings the estimate closer to the actual root, demonstrating the effectiveness of this technique. The Newton-Raphson method is a classic example of successive approximation, where the solution is approached through tangent lines.Similarly, in engineering, successive approximation plays a crucial role in design and testing. Engineers often utilize prototyping to develop new products. The first prototype may not meet all specifications or user needs, but through testing and feedback, engineers make successive changes and improvements. Each version of the prototype is an approximation of the final product, and this iterative process helps ensure that the end result is both functional and user-friendly.In the realm of psychology, successive approximation is foundational to behavioral techniques such as shaping. When training animals or modifying human behavior, trainers often reward successive behaviors that are closer to the desired action. For example, if a trainer wants a dog to roll over, they might first reward it for lying down, then for rolling onto its side, and finally for completing the roll. This method of reinforcing small steps leads to the eventual achievement of the target behavior, illustrating how successive approximation can facilitate learning and development.Moreover, successive approximation can be applied in personal goal-setting and self-improvement. Instead of attempting to achieve a significant change all at once, individuals can set smaller, achievable milestones. For example, someone aiming to lose weight might start by making minor adjustments to their diet and exercise routine rather than overhauling their lifestyle overnight. Each small success builds confidence and momentum, leading to more substantial changes over time.In conclusion, the principle of successive approximation is a powerful approach that transcends various disciplines. Whether in mathematics, engineering, psychology, or personal growth, the idea of making gradual improvements through incremental steps can lead to successful outcomes. By embracing this method, individuals and professionals alike can tackle complex challenges with greater ease and efficiency. Ultimately, successive approximation teaches us that progress does not always have to be swift; rather, it can be a series of small, deliberate steps towards achieving our goals.

“逐次逼近”的概念是多个领域中一个重要的原则，包括数学、工程和心理学。它指的是通过逐步调整或增量步骤逐渐接近所需结果或目标的过程。这种方法在处理复杂问题时尤其有用，因为直接解决方案并不总是可用。通过将问题分解为更小、更易管理的组成部分，个人可以稳步向目标迈进。在数学中，“逐次逼近”通常用于数值方法，以寻找无法解析地解决的方程的解。例如，当试图确定多项式的根时，人们可能会从初始猜测开始，然后根据函数的行为来精炼该猜测。每次迭代都使估计值更接近实际根，展示了这一技术的有效性。牛顿-拉夫森法是“逐次逼近”的经典例子，通过切线的方法接近解决方案。同样，在工程中，“逐次逼近”在设计和测试中也起着至关重要的作用。工程师通常利用原型开发新产品。第一个原型可能无法满足所有规格或用户需求，但通过测试和反馈，工程师会进行逐步的更改和改进。每个版本的原型都是最终产品的一个近似，这一迭代过程有助于确保最终结果既功能齐全又用户友好。在心理学领域，“逐次逼近”是行为技术（如塑造）的基础。当训练动物或修改人类行为时，训练者通常会奖励越来越接近所需行为的逐步行为。例如，如果训练者想要狗翻滚，他们可能首先奖励狗躺下，然后奖励狗翻到侧面，最后奖励狗完成翻滚。这种强化小步骤的方法导致最终实现目标行为，说明了“逐次逼近”如何促进学习和发展。此外，“逐次逼近”还可以应用于个人目标设定和自我改善。与其试图一次性实现重大变化，不如设定较小、可实现的里程碑。例如，想减肥的人可能会先对饮食和锻炼习惯进行小幅调整，而不是一夜之间彻底改变生活方式。每一个小成功都能建立信心和动力，从而在一段时间内实现更大的变化。总之，“逐次逼近”的原则是一种强大的方法，超越了各个学科。无论是在数学、工程、心理学还是个人成长中，通过逐步改进的增量步骤的理念都能带来成功的结果。通过接受这种方法，个人和专业人士都可以更轻松、高效地应对复杂挑战。最终，“逐次逼近”教会我们，进步不一定要迅速；相反，它可以是朝着实现目标的一系列小而有意识的步骤。