Numerical Analysis Lecture Notes
Peter J. Olver
7. Iterative Methods for Linear Systems
Linear iteration coincides with multiplication by successive powers of a matrix; convergence of the iterates dep
Numerical Analysis Lecture Notes
Peter J. Olver
4. Gaussian Elimination
In this part, our focus will be on the most basic method for solving linear algebraic
systems, known as Gaussian Elimination in
Numerical Analysis Lecture Notes
Peter J. Olver
8. Numerical Computation of Eigenvalues
In this part, we discuss some practical methods for computing eigenvalues and eigenvectors of matrices. Needless
Numerical Analysis Lecture Notes
Peter J. Olver
13. Approximation and Interpolation
We will now apply our minimization results to the interpolation and least squares
tting of data and functions.
13.1.
Numerical Analysis Lecture Notes
Peter J. Olver
5. Inner Products and Norms
The norm of a vector is a measure of its size. Besides the familiar Euclidean norm
based on the dot product, there are a num
Numerical Analysis Lecture Notes
Peter J. Olver
3. Review of Matrix Algebra
Vectors and matrices are essential for modern analysis of systems of equations
algebrai, dierential, functional, etc. In th
Numerical Analysis Lecture Notes
Peter J. Olver
12. Minimization
In this part, we will introduce and solve the most basic mathematical optimization
problem: minimize a quadratic function depending on
Numerical Analysis Lecture Notes
Peter J. Olver
11. Finite Dierence Methods for
Partial Dierential Equations
As you are well aware, most dierential equations are much too complicated to be
solved by a
Numerical Analysis Lecture Notes
Peter J. Olver
14. Finite Elements
In this part, we introduce the powerful nite element method for nding numerical
approximations to the solutions to boundary value pr
Numerical Analysis Lecture Notes
Peter J. Olver
1. Computer Arithmetic
The purpose of computing is insight, not numbers.
R.W. Hamming, [24]
The main goal of numerical analysis is to develop ecient al
Numerical Analysis Lecture Notes
Peter J. Olver
6. Eigenvalues and Singular Values
In this section, we collect together the basic facts about eigenvalues and eigenvectors.
From a geometrical viewpoint
Numerical Analysis Lecture Notes
Peter J. Olver
9. Numerical Solution of Algebraic Systems
In this part, we discuss basic iterative methods for solving systems of algebraic equations. By far the most
Numerical Analysis Lecture Notes
Peter J. Olver
10. Numerical Solution of
Ordinary Dierential Equations
This part is concerned with the numerical solution of initial value problems for systems
of ordi