Basic Numerical Methods: Numerical Analysis for M/c Learning
1 : Basic Numerical Methods: Numerical Analysis for M/c Learning
Numerical Methods: Learn Basics of Numerical Analysis for Deep learning, Machine Learning , AI and Data Science
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Numerical methods play a critical role in machine learning, deep learning, artificial intelligence, and data science. These methods are essential for solving complex mathematical problems that are common in these fields.
One of the most important uses of numerical methods in these areas is in the optimization of machine learning models. Optimization is the process of finding the set of model parameters that minimize a given objective function. This process involves complex mathematical calculations that often require numerical methods such as gradient descent, Newton's method, and conjugate gradient methods.
Numerical methods are also used in the analysis of large datasets. Data scientists often encounter datasets that are too large to be processed using traditional methods. In these cases, numerical methods such as randomized linear algebra and Monte Carlo simulations can be used to efficiently process the data.
Another important use of numerical methods in these areas is in the simulation of complex systems. Simulations are used to model the behavior of complex systems such as weather patterns, financial markets, and biological systems. Numerical methods such as finite element methods, spectral methods, and stochastic simulations are essential for accurately simulating these systems.
Here , in this course you'll receive support through a Q and A section, and the course is continually updated based on student feedback, with plans to add new topics in the future.
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What you'll learn
- Understand how Numerical Methods fits into the broader context of computer science
- Develop a deep understanding of the concepts of numerical analysis
- Learn how to interpret formulae and understand practical approach
- Learn how to deal with common issues in numerical methods
Requirements
- High school knowledge of Math and specially calculus
Numerical methods in finance include finite difference methods, and statisti- cal and Monte Carlo methods for computation of option prices and hedging strategies. This chapter is a basic introduction to finite difference methods for the resolution of PDEs and stochastic differential equations.
Numerical analysis forms the foundation of many of the machine learning algorithms. Therefore, in the last chapter of the 2nd part of the book, we will introduce you some of the basic machine learning problems as a motivation for you to learn more tools and skills to solve problems in the future.
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Numerical analysis is a branch of mathematics that solves continuous problems using numeric approximation. It involves designing methods that give approximate but accurate numeric solutions, which is useful in cases where the exact solution is impossible or prohibitively expensive to calculate.
Numerical analysis is employed to develop and analyze numerical methods for solving problems that arise in other areas of mathematics, such as calculus, linear algebra, or differential equations. Of course, these areas already include methods for solving such problems, but these are analytical in nature.
If the functions are known analytically instead of being tabulated at equally spaced intervals, the best numerical method of integration is called Gaussian quadrature. By picking the abscissas at which to evaluate the function, Gaussian quadrature produces the most accurate approximations possible.
What are the different types of numerical analysis? The different types of numerical analysis are finite difference methods, propagation of errors, interpolation methods, and so on.
The Monte Carlo method is a numerical method of solving mathematical problems by random sampling (or by the simulation of random variables).
-Abstract : Probabilistic numerical methods are at the heart of machine learning algorithms. They play an important role in related optimization problems and also certainly for sampling methods which can be used for calibration, generation of new datas or sensitivity problems (among other applications).
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In the machine learning world, data is nearly always split into two groups: numerical and categorical. Numerical data is used to mean anything represented by numbers (floating point or integer). Categorical data generally means everything else and in particular discrete labeled groups are often called out.
Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
Numerical-software packages. Analytica is a widely used proprietary tool for building and analyzing numerical models. It is a declarative and visual programming language based on influence diagrams. FlexPro is a program for data analysis and presentation of measurement data.
A numerical method is said to be consistent if all the approximations (finite difference, finite element, finite volume etc) of the derivatives tend to the exact value as the step size (∆t, ∆x etc) tends to zero.
INSTRUCTOR
Sandeep Kumar Mathur
