bilinear
简明释义
adj. 双线性的
英英释义
单词用法
双线性插值 | |
双线性变换 |
同义词
反义词
线性的 | 变量之间的关系是线性的。 | ||
非线性的 | 非线性方程可能更复杂,难以解决。 |
例句
1.In this paper, we discuss the stationarity and invertibility of a bilinear model.
本文主要讨论双线性时间序列模型的平稳性与可逆性。
2.A threshold signature scheme based on the bilinear mapping tool was proposed.
使用双线性映射工具,提出基于双线性对的门限签名方案。
3.This paper mainly does some research in applications of constructing new cryptographic protocols with bilinear pairings.
本文主要研究双线性配对函数在构造新的密码协议方面的应用。
4.The optimal control problem is considered for bilinear systems affected by external persistent disturbances.
研究具有外界持续扰动作用下双线性系统的最优控制问题。
5.The problem of designing an observer for bilinear multivariable systems in the presence of unknown disturbances is considered.
本文讨论了存在未知扰动情况下如何设计双线性多变量系统的观测器问题。
6.An experimental model for studying the dynamic response of bilinear hysteretic system is developed.
本文介绍一个研究双线性滞后系统响应的实验装置。
7.The main mathematical tool of this method is bilinear interpolation.
该方法的主要数学工具是双线性插值。
8.The paper based on genetic algorithms proposes a method for identification of bilinear discrete dynamic model parameters.
本文以遗传算法为基础,提出了一种辨识双线性离散动态系统模型参数的方法。
9.The function is defined as a bilinear 双线性 map between two vector spaces.
这个函数被定义为两个向量空间之间的双线性映射。
10.In image processing, bilinear 双线性 interpolation is often used to resize images smoothly.
在图像处理中,双线性插值常用于平滑地调整图像大小。
11.The bilinear 双线性 form allows for the representation of quadratic surfaces in three-dimensional space.
该双线性形式允许在三维空间中表示二次曲面。
12.Using bilinear 双线性 regression can help model the relationship between two variables more accurately.
使用双线性回归可以更准确地建模两个变量之间的关系。
13.The software includes a bilinear 双线性 filter to enhance video quality during playback.
该软件包括一个双线性滤镜,以在播放过程中增强视频质量。
作文
In the realm of mathematics and computer science, the concept of bilinear (双线性) functions plays a crucial role in various applications. To understand what bilinear means, we need to delve into its definition and significance. A bilinear function is one that is linear in each of its arguments when the other argument is held fixed. This property makes bilinear functions particularly useful in areas such as optimization, image processing, and machine learning. For instance, consider a simple example involving two variables, x and y. A function f(x, y) is bilinear if, for any fixed value of y, the function f(x, y) behaves like a linear function of x. Similarly, if we fix x, then f(x, y) behaves like a linear function of y. This duality is what characterizes bilinear functions and sets them apart from other types of functions. One common application of bilinear functions is in the field of image processing. When manipulating images, it is often necessary to resize or rotate them. The bilinear interpolation technique is frequently employed for these tasks. This method considers the closest four pixels surrounding a desired pixel location and calculates the new pixel value based on a weighted average of these neighboring pixels. The result is a smoother and more visually appealing image compared to simpler methods like nearest-neighbor interpolation. Another important area where bilinear functions are applied is in the optimization of multi-variable systems. In operations research, for example, problems often involve maximizing or minimizing a function that depends on two or more variables. By using bilinear programming techniques, one can effectively solve complex optimization problems where the relationships between variables are not merely linear but exhibit bilinear characteristics. Furthermore, bilinear forms arise in various mathematical contexts, such as in the study of quadratic forms and in defining certain types of matrices. The properties of bilinear forms allow mathematicians to explore deeper connections between different areas of mathematics, including algebra and geometry. In conclusion, the term bilinear (双线性) encapsulates a fundamental concept that bridges multiple disciplines. Its applications in image processing, optimization, and mathematical theory demonstrate its versatility and importance. Understanding bilinear functions not only enhances our grasp of mathematical principles but also equips us with powerful tools for solving real-world problems. As technology continues to advance, the relevance of bilinear functions will undoubtedly persist, making it an essential topic for students and professionals alike to master.
在数学和计算机科学领域,bilinear(双线性)函数的概念在各种应用中发挥着至关重要的作用。要理解bilinear的含义,我们需要深入其定义和重要性。bilinear函数是指在固定其他参数时,对于每个参数都是线性的函数。这一特性使得bilinear函数在优化、图像处理和机器学习等领域特别有用。 例如,考虑一个涉及两个变量x和y的简单例子。如果f(x, y)是bilinear的,那么对于任何固定的y,函数f(x, y)在x上表现得像一个线性函数。类似地,如果我们固定x,那么f(x, y)在y上表现得也像一个线性函数。这种对偶性正是bilinear函数的特征,使其与其他类型的函数区分开来。 bilinear函数的一个常见应用是在图像处理领域。当操控图像时,通常需要对其进行缩放或旋转。bilinear插值技术常用于这些任务。该方法考虑到目标像素位置周围最近的四个像素,并根据这些邻近像素的加权平均值计算新的像素值。与更简单的方法如最近邻插值相比,这样的结果能够生成更平滑、更具视觉吸引力的图像。 bilinear函数的另一个重要应用是在多变量系统的优化中。例如,在运筹学中,问题通常涉及最大化或最小化一个依赖于两个或多个变量的函数。通过使用bilinear规划技术,可以有效地解决复杂的优化问题,这些问题的变量之间的关系不仅仅是线性的,而是具有bilinear特征。 此外,bilinear形式出现在多种数学背景中,例如在二次形式的研究以及定义某些类型的矩阵时。bilinear形式的性质使数学家能够探索不同数学领域之间更深层次的联系,包括代数和几何。 总之,术语bilinear(双线性)概括了一个基本概念,它连接了多个学科。它在图像处理、优化和数学理论中的应用展示了其多功能性和重要性。理解bilinear函数不仅增强了我们对数学原理的掌握,而且为我们提供了强大的工具,以解决现实世界中的问题。随着科技的不断进步,bilinear函数的相关性无疑将持续存在,使其成为学生和专业人士必须掌握的重要主题。
文章标题:bilinear的意思是什么
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