This is an exhaustive PDF written by Lars Elden, Linde Wittmeyer-Koch,
and Hans Bruun Nielsen. In fact, this really is an exemplary introduction to
numerical computation. The text begins with the basics like error analysis and
computer arithmetic, which gives a very solid ground for the origin and handling
of numerical errors. It proceeds further to explain more basic topics related to
function evaluation, solutions of nonlinear equations, and interpolation
techniques. Next, it describes procedures for improving numerical estimates
using differentiation and Richardson extrapolation. This is followed by full
details of integration, systems of linear equations, and approximation. Finally,
ordinary differential equations complete a thorough course of study that will
prepare the reader with both the theory and practice that will serve in carrying
out numerical computations.
Author(s): Lars Elden, Linde Wittmeyer-Koch, Hans
Bruun Nielsen
This is an exhaustive PDF written by Lars Elden, Linde Wittmeyer-Koch,
and Hans Bruun Nielsen. In fact, this really is an exemplary introduction to
numerical computation. The text begins with the basics like error analysis and
computer arithmetic, which gives a very solid ground for the origin and handling
of numerical errors. It proceeds further to explain more basic topics related to
function evaluation, solutions of nonlinear equations, and interpolation
techniques. Next, it describes procedures for improving numerical estimates
using differentiation and Richardson extrapolation. This is followed by full
details of integration, systems of linear equations, and approximation. Finally,
ordinary differential equations complete a thorough course of study that will
prepare the reader with both the theory and practice that will serve in carrying
out numerical computations.
Author(s): Lars Elden, Linde Wittmeyer-Koch, Hans
Bruun Nielsen
Prof. L. Vandenberghe's lecture note is on applied numerical
computing but brings out the practical application aspect. The text covers most
areas of numerical linear algebra, nonlinear optimization nonlinear least
squares, introduction to floating-point numbers, and rounding errors that are to
be needed for understanding the issues of numerical precision. Examples are
drawn from signal and image processing, control systems, and machine learning,
among other areas, to indicate how these numerical methods are actually applied.
This resource aims to fill the gap between theory and practice by providing a
practical method for solving computational problems.
The
resource described here is an overview of numerical methods important in the
study of computational science and engineering. The text starts off with
Computing with Matrices and Vectors, foundational elements in many algorithms.
The note moves forward and explains Direct Methods for Linear Systems of
Equations and Direct Methods for Linear Least Squares Problems, important
problem-solving aspects in linear algebra. The Filtering Algorithms for data
processing are reviewed, while Data Interpolation and Data Fitting in 1D discuss
ways of approximating onedimensional data. Approximation of Functions in 1D and
Numerical Quadrature introduce the techniques on function approximation and
integration. It also discusses Iterative Methods for Non-Linear Systems of
Equations and Eigenvalues-a critical topic needed for solving complex systems.
It finally includes Numerical Integration and Structure Preserving Integration,
fundamental to perform numerical calculations with appropriate accuracy in
scientific computing.
This
lecture series provides comprehensive foundational knowledge in the field of
numerical computational analysis. Numerical Linear Algebra covers basic matrix
operations and solutions of linear systems. The book further goes into the
Solution of Nonlinear Equations that shows methods for solving equations which
are not linear in form. Finally, it discusses Approximation Theory, showing how
functions and data may be approximated. The lectures also cover Numerical
Solution of ODEs and PDEs, giving ways to solve these two basic kinds of
equations. This resource is intended for students and professionals looking to
gain a solid understanding of basic and applied numerical analysis techniques.