<?xml version="1.0" encoding="utf-8" ?><rss version="2.0"><channel><title><![CDATA[zhangmohan123321的博客]]></title><description><![CDATA[]]></description><link>https://blog.youkuaiyun.com/zhangmohan123321</link><language>zh-cn</language><generator>https://blog.youkuaiyun.com/</generator><copyright><![CDATA[Copyright &copy; zhangmohan123321]]></copyright><item><title><![CDATA[【拟牛顿法】DFP与BFGS算法]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/156021360</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/156021360</guid><author>zhangmohan123321</author><pubDate>Wed, 17 Dec 2025 16:37:40 +0800</pubDate><description><![CDATA[本文详解 DFP、BFGS 拟牛顿法，推导其海森（逆）近似矩阵秩 2 修正公式，结合二次函数、Rosenbrock 函数实例与 Python 代码，对比两种算法的收敛性能与应用特点。]]></description><category></category></item><item><title><![CDATA[【深度学习】LSTM长短期记忆网络]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155075536</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155075536</guid><author>zhangmohan123321</author><pubDate>Thu, 20 Nov 2025 20:37:57 +0800</pubDate><description><![CDATA[LSTM是RNN的变体，通过遗忘、输入和输出门以及记忆元解决长序列依赖中的梯度消失问题。其核心是记忆元的加法更新，确保信息稳定传递，广泛应用于NLP、语音识别和时间序列预测等领域。]]></description><category></category></item><item><title><![CDATA[【深度学习】GAN生成对抗网络]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155075383</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155075383</guid><author>zhangmohan123321</author><pubDate>Thu, 20 Nov 2025 20:29:55 +0800</pubDate><description><![CDATA[GAN通过生成器（G）与判别器（D）的对抗性博弈训练。目标是使G生成逼真样本，D无法区分真假。核心挑战包括梯度消失和模式崩塌，WGAN-GP和StyleGAN是重要改进。]]></description><category></category></item><item><title><![CDATA[【深度学习】RNN循环神经网络]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155075052</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155075052</guid><author>zhangmohan123321</author><pubDate>Thu, 20 Nov 2025 20:12:51 +0800</pubDate><description><![CDATA[RNN 专用于处理序列数据，通过循环连接实现信息记忆和参数共享。标准RNN受限于梯度消失。LSTM/GRU引入门控机制解决此问题，是序列建模的核心模型。]]></description><category></category></item><item><title><![CDATA[【深度学习】CNN卷积神经网络]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074960</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074960</guid><author>zhangmohan123321</author><pubDate>Thu, 20 Nov 2025 20:04:20 +0800</pubDate><description><![CDATA[卷积神经网络（CNN）通过局部连接和权值共享高效提取图像特征。核心组件包括卷积层、激活层、池化层。ResNet等引入残差连接深化网络。实践中常使用数据增强和迁移学习优化模型，广泛应用于图像识别和目标检测。]]></description><category></category></item><item><title><![CDATA[【有约束优化】投影法]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074728</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074728</guid><author>zhangmohan123321</author><pubDate>Thu, 20 Nov 2025 19:50:54 +0800</pubDate><description><![CDATA[投影法：沿着下降方向移动后，将点投影回可行集。]]></description><category></category></item><item><title><![CDATA[【有约束优化】罚函数法]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074612</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074612</guid><author>zhangmohan123321</author><pubDate>Thu, 20 Nov 2025 19:45:30 +0800</pubDate><description><![CDATA[惩罚函数法将约束优化转为无约束问题。序列惩罚易导致病态性，精确惩罚不可微。增广拉格朗日法克服病态性，是高效的混合方法。]]></description><category></category></item><item><title><![CDATA[【有约束优化】拉格朗日法]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074245</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/155074245</guid><author>zhangmohan123321</author><pubDate>Thu, 20 Nov 2025 19:36:37 +0800</pubDate><description><![CDATA[拉格朗日法求解等式约束优化，通过构造拉格朗日函数，利用梯度平行求驻点。推广至不等式约束，需应用KKT 条件（驻点、原始/对偶可行性、互补松弛性）。凸规划中，KKT条件是全局最优的充分必要条件。]]></description><category></category></item><item><title><![CDATA[【无约束优化】多维搜索——梯度方法]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/152663478</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/152663478</guid><author>zhangmohan123321</author><pubDate>Tue, 07 Oct 2025 16:04:14 +0800</pubDate><description><![CDATA[梯度方法通过沿函数下降最快方向迭代搜索最优解，原理简单直观，但收敛速度较慢，对步长敏感，常作为更优算法的基础。]]></description><category></category></item><item><title><![CDATA[【无约束优化】无约束优化之一维搜索]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/152663263</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/152663263</guid><author>zhangmohan123321</author><pubDate>Tue, 07 Oct 2025 15:50:16 +0800</pubDate><description><![CDATA[本文详解一维搜索三大类方法：直接法（黄金分割、斐波那契）、导数法（二分法）、插值法（牛顿法、割线法），涵盖原理、公式、例子与对比。]]></description><category></category></item><item><title><![CDATA[【多项式】快速沃尔什变换 (FWT)]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151019881</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151019881</guid><author>zhangmohan123321</author><pubDate>Sat, 30 Aug 2025 19:30:00 +0800</pubDate><description><![CDATA[快速沃尔什变换（FWT）是一种高效计算按位运算卷积的算法，适用于异或、与、或三种运算。其核心思想是通过线性变换将卷积转化为逐点乘积，类似FFT处理加法卷积的方式。FWT采用分治策略，对序列进行变换和逆变换，其中异或卷积最复杂，需使用Walsh-Hadamard变换。三种运算分别对应不同的变换矩阵和分治方法，并可通过C++实现高效计算。FWT在组合数学、算法竞赛等领域有重要应用。]]></description><category></category></item><item><title><![CDATA[【树形数据结构】李超线段树 (Li-Chao Tree)]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151020974</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151020974</guid><author>zhangmohan123321</author><pubDate>Sat, 30 Aug 2025 16:25:15 +0800</pubDate><description><![CDATA[李超线段树通过在每个区间维护中点最优线段，支持高效动态插入线段与单点最值查询，结合离散化可处理大坐标范围，常用于斜率优化等场景。]]></description><category></category></item><item><title><![CDATA[【多项式】快速莫比乌斯变换（FMT）]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151019609</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151019609</guid><author>zhangmohan123321</author><pubDate>Sat, 30 Aug 2025 15:09:47 +0800</pubDate><description><![CDATA[FMT通过按集合大小分层并进行子集和变换，将子集卷积从O(3^n)优化至O(n²2^n)，高效处理集合不相交合并问题。]]></description><category></category></item><item><title><![CDATA[【图论】分层图]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151001464</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/151001464</guid><author>zhangmohan123321</author><pubDate>Sat, 30 Aug 2025 02:06:35 +0800</pubDate><description><![CDATA[分层图通过将状态拆解为多层结构，利用层内/层间边建模状态转移，结合最短路径算法（如Dijkstra）解决复杂问题，适用于有限次决策或状态依赖场景，如飞行路线优化与时间余数分层问题。]]></description><category></category></item><item><title><![CDATA[【树论】树上启发式合并]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150999190</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150999190</guid><author>zhangmohan123321</author><pubDate>Fri, 29 Aug 2025 23:59:50 +0800</pubDate><description><![CDATA[树上启发式合并（DSU on Tree）通过保留重儿子信息、合并轻儿子，高效处理子树查询，时间复杂度 $O(n \log n)$，适用于离线统计问题。]]></description><category></category></item><item><title><![CDATA[【数论】扩展欧几里德算法]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150965705</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150965705</guid><author>zhangmohan123321</author><pubDate>Thu, 28 Aug 2025 23:33:00 +0800</pubDate><description><![CDATA[扩展欧几里德算法在求最大公约数的同时，求解ax+by=gcd(a,b)的整数解，是求模逆元、解线性同余方程的基础，时间复杂度O(log n)。]]></description><category></category></item><item><title><![CDATA[【多项式】快速傅里叶变换（FFT）]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150965007</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150965007</guid><author>zhangmohan123321</author><pubDate>Thu, 28 Aug 2025 22:56:58 +0800</pubDate><description><![CDATA[FFT通过分治法将DFT的O(N²)复杂度降至O(N log N)，核心是蝶形运算与位逆序重排，广泛应用于信号处理、多项式乘法等领域。]]></description><category></category></item><item><title><![CDATA[【线性数据结构】颜色段均摊（珂朵莉树 ODT）]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150945769</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150945769</guid><author>zhangmohan123321</author><pubDate>Thu, 28 Aug 2025 10:31:40 +0800</pubDate><description><![CDATA[珂朵莉树利用区间赋值次数少的特性，将序列划分为连续同值段，通过分裂与合并操作，均摊处理复杂区间查询，适用于非线性操作。]]></description><category></category></item><item><title><![CDATA[【线性数据结构】差分]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150937637</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150937637</guid><author>zhangmohan123321</author><pubDate>Wed, 27 Aug 2025 23:20:31 +0800</pubDate><description><![CDATA[差分通过构建差值数组，将区间修改转化为单点操作，实现O(1)更新与O(n)还原，常用于高效处理批量区间增减问题。]]></description><category></category></item><item><title><![CDATA[【树论】树的重心]]></title><link>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150867708</link><guid>https://blog.youkuaiyun.com/zhangmohan123321/article/details/150867708</guid><author>zhangmohan123321</author><pubDate>Tue, 26 Aug 2025 23:30:00 +0800</pubDate><description><![CDATA[树的重心是使最大子树最小的节点，最多两个且相邻。通过DFS计算子树大小，考虑父方向分量，O(n)求解，用于树分治等。]]></description><category></category></item></channel></rss>