Numerical Methods with Artificial Intelligence Applications

Advanced Optimization, Deep Learning, and Intelligent Computing (Vol. 2)

Artificial Intelligence has evolved beyond traditional algorithms into an era of large-scale optimization, deep neural networks, probabilistic reasoning, scientific computing, and intelligent automation. Behind every successful AI system lies a foundation of efficient numerical algorithms capable of solving complex mathematical problems under real-world computational constraints.

Numerical Methods with Artificial Intelligence Applications: Advanced Optimization, Deep Learning, and Intelligent Computing (Vol. 2) builds upon the concepts introduced in Volume 1 and takes readers into the advanced world of numerical computation for Artificial Intelligence. The book integrates classical numerical analysis with state-of-the-art AI techniques, enabling readers to understand how optimization algorithms, numerical linear algebra, probabilistic computation, and deep learning work together to create intelligent systems.

This volume emphasizes practical applications, algorithmic understanding, computational efficiency, and modern AI implementation. Each chapter combines mathematical concepts with real-world machine learning and deep learning examples, making the book suitable for academic learning, research, and industry practice.

What You’ll Learn

✔ Constrained Optimization Techniques

✔ Equality and Inequality Constraints

✔ Lagrange Multiplier Method

✔ Karush–Kuhn–Tucker (KKT) Conditions

✔ Penalty and Barrier Methods

✔ Regularized Machine Learning

✔ Batch, Stochastic and Mini-Batch Gradient Descent

✔ Momentum Optimization

✔ Adam Optimizer

✔ RMSProp

✔ AdaGrad

✔ Numerical Linear Algebra

✔ Gaussian Elimination

✔ LU Decomposition

✔ QR Decomposition

✔ Iterative Linear Solvers

✔ Eigenvalues and Eigenvectors

✔ Singular Value Decomposition (SVD)

✔ Principal Component Analysis (PCA)

✔ Dimensionality Reduction

✔ Numerical Methods in Deep Learning

✔ Backpropagation Algorithms

✔ Hessian-Based Optimization

✔ Vanishing Gradient Problem

✔ Exploding Gradient Problem

✔ Numerical Stability in Neural Networks

✔ Genetic Algorithms

✔ Particle Swarm Optimization

✔ Differential Evolution

✔ Probabilistic Artificial Intelligence

✔ Markov Chain Monte Carlo (MCMC)

✔ Variational Inference

✔ Bayesian Approximation

✔ Numerical Sampling

✔ Python for Numerical Computing

✔ NumPy Programming

✔ SciPy Numerical Libraries

✔ TensorFlow Optimization

✔ PyTorch Machine Learning

✔ AI Performance Optimization

✔ Neural Network Training

✔ Time Series Forecasting

✔ Image Processing

✔ Signal Processing

✔ Healthcare Artificial Intelligence

✔ Financial AI Applications

✔ Large-Scale Optimization

✔ Distributed Numerical Computing

✔ Parallel Numerical Algorithms

✔ Quantum Numerical Computing

✔ Hybrid Symbolic AI

✔ Automated Optimization Systems

Chapter 14

Constrained Optimization Techniques

Chapter 15

Optimization Algorithms for Machine Learning

Chapter 16

Numerical Linear Algebra for Artificial Intelligence

Chapter 17

Eigenvalues and Matrix Factorization

Chapter 18

Numerical Methods in Deep Learning

Chapter 19

Evolutionary and Swarm-Based Optimization

Chapter 20

Numerical Methods in Probabilistic Artificial Intelligence

Chapter 21

Implementation Using Python and AI Libraries

Chapter 22

Case Studies and Real-World AI Applications

Chapter 23

Numerical Challenges in Modern Artificial Intelligence

Chapter 24

Future Scope and Research Directions

Who Should Read This Book?

This book is ideal for:

B.Tech Students
BCA Students
MCA Students
B.Sc. Computer Science Students
B.Sc. Information Technology Students
M.Tech Students
Artificial Intelligence Students
Machine Learning Engineers
Deep Learning Researchers
Data Scientists
Software Engineers
AI Researchers
University Faculty
Research Scholars
Scientific Computing Professionals
Engineering Professionals
Competitive Examination Aspirants

Key Features

✅ Advanced Numerical Optimization Techniques

✅ AI and Machine Learning Applications

✅ Deep Learning Optimization Methods

✅ Python Implementation with NumPy and SciPy

✅ TensorFlow and PyTorch Examples

✅ Linear Algebra for Artificial Intelligence

✅ Real-World AI Case Studies

✅ Scientific Computing Applications

✅ Research-Oriented Content

✅ Industry-Relevant Algorithms

✅ Beginner to Advanced Learning Path

✅ University Curriculum Aligned

✅ Excellent for Research, Projects, and Self-Learning

Why This Book?

Artificial Intelligence is fundamentally driven by numerical computation. Modern AI systems depend on optimization algorithms, matrix factorization, probabilistic inference, gradient-based learning, and large-scale numerical techniques to achieve intelligent behavior.

Unlike traditional numerical analysis books, this volume focuses specifically on how numerical methods are applied in Machine Learning, Deep Learning, Data Science, Scientific Computing, and Artificial Intelligence. Readers gain not only theoretical knowledge but also practical insights into implementing numerical algorithms using modern AI frameworks such as Python, NumPy, SciPy, TensorFlow, and PyTorch.

Whether you are preparing for university examinations, conducting research, developing AI applications, or enhancing your computational mathematics skills, this book provides a comprehensive and industry-oriented resource.

Book Details

Title: Numerical Methods with Artificial Intelligence Applications

Subtitle: Advanced Optimization, Deep Learning, and Intelligent Computing

Volume: Vol. 2

Author: Anshuman Mishra

Publisher: Anshuman Mishra

Publication Year: 2025

Gaussian Elimination

Numerical Methods with Artificial Intelligence Applications VOL-2