VIP内容

使用C编程语言学习应用数值计算,从快速入门的C编程语言及其SDK开始。然后,这本书深入到使用C的计算方法的渐进更复杂的应用数学公式的例子贯穿始终,并在最后一个更大的,更完整的应用。

Numerical C以二次公式开始,用于寻找代数方程的解,这些代数方程模拟诸如价格与需求、上涨与运行或下滑等情况。在本书后面,你将学习联立方程的增广矩阵法。

您还将介绍蒙特卡罗方法模型对象,这些对象可以作为真实系统建模的一部分自然产生,例如复杂的道路网络、中子的传输或股票市场的演化。此外,蒙特卡罗方法的集成检查曲线下的面积,包括渲染或射线跟踪和一个地区的阴影。

此外,您将使用积差相关系数:相关是一种用于研究两个定量连续变量(例如年龄和血压)之间关系的技术。在这本书的最后,你会有一个感觉,什么电脑软件可以做,以帮助你在你的工作和应用一些方法直接学习到你的工作。

你会学到什么

  • 获得软件和C语言编程基础
  • 编写软件解决应用,计算数学问题
  • 创建程序来解决方程和微积分问题
  • 采用梯形法、蒙特卡罗法、最佳拟合线、积差相关系数、辛普森法则和矩阵解法
  • 写代码来解微分方程
  • 将一个或多个方法应用到应用案例研究中

这本书是给谁看的

具有基本数学知识(学校水平)和一些基本编程经验的人。这对于那些可能在数学或其他领域(例如,生命科学、工程或经济学)工作并需要学习C编程的人来说也很重要。

成为VIP会员查看完整内容
0
41

热门内容

Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this variable using data generated during the course of a traditional numerical method. However, data may be nonlinearly related to the quantity of interest, rendering the proper conditioning of random variables difficult and limiting the range of numerical tasks that can be addressed. Instead, this paper proposes to construct probabilistic numerical methods based only on the final output from a traditional method. A convergent sequence of approximations to the quantity of interest constitute a dataset, from which the limiting quantity of interest can be extrapolated, in a probabilistic analogue of Richardson's deferred approach to the limit. This black box approach (1) massively expands the range of tasks to which probabilistic numerics can be applied, (2) inherits the features and performance of state-of-the-art numerical methods, and (3) enables provably higher orders of convergence to be achieved. Applications are presented for nonlinear ordinary and partial differential equations, as well as for eigenvalue problems-a setting for which no probabilistic numerical methods have yet been developed.

0
0
下载
预览

最新内容

We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large dimension of the dynamical system state poses a computational obstacle to computing the exact posterior distribution. Model reduction offers a variety of computational tools that seek to reduce this computational burden. In particular, balanced truncation is a system-theoretic approach to model reduction which obtains an efficient reduced-dimension dynamical system by projecting the system operators onto state directions which trade off the reachability and observability of state directions as expressed through the associated Gramians. We introduce Gramian definitions relevant to the inference setting and propose a balanced truncation approach based on these inference Gramians that yield a reduced dynamical system that can be used to cheaply approximate the posterior mean and covariance. Our definitions exploit natural connections between (i) the reachability Gramian and the prior covariance and (ii) the observability Gramian and the Fisher information. The resulting reduced model then inherits stability properties and error bounds from system theoretic considerations, and in some settings yields an optimal posterior covariance approximation. Numerical demonstrations on two benchmark problems in model reduction show that our method can yield near-optimal posterior covariance approximations with order-of-magnitude state dimension reduction.

0
0
下载
预览

最新论文

We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large dimension of the dynamical system state poses a computational obstacle to computing the exact posterior distribution. Model reduction offers a variety of computational tools that seek to reduce this computational burden. In particular, balanced truncation is a system-theoretic approach to model reduction which obtains an efficient reduced-dimension dynamical system by projecting the system operators onto state directions which trade off the reachability and observability of state directions as expressed through the associated Gramians. We introduce Gramian definitions relevant to the inference setting and propose a balanced truncation approach based on these inference Gramians that yield a reduced dynamical system that can be used to cheaply approximate the posterior mean and covariance. Our definitions exploit natural connections between (i) the reachability Gramian and the prior covariance and (ii) the observability Gramian and the Fisher information. The resulting reduced model then inherits stability properties and error bounds from system theoretic considerations, and in some settings yields an optimal posterior covariance approximation. Numerical demonstrations on two benchmark problems in model reduction show that our method can yield near-optimal posterior covariance approximations with order-of-magnitude state dimension reduction.

0
0
下载
预览
Top