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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
A. Quadratic form minimum.
B. Method of steepest descent.
C. Method of conjugate directions.
D. Method of conjugate gradients.
E. Convergence analysis of conjugate gradient method.
F. Preconditioning.
G. Recursive calculation.
H. Parallel subspace preconditioner.
2. Wavelet Analysis.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Calculational Linear Algebra.


he reference, unless stated otherwise, is [Schewchuk] .

The primary interest of this chapter is solving a linear equation of the form

MATH (Linear equation)
Most of the time $A$ is symmetric positive definite or, at least, symmetric. We will be interested in extension to more generic matrixes as well. The solution $x^{\ast}$ is the equation ( Linear equation ) will be approximated with some sequence MATH , MATH with a property MATH . In such context we will be using the notations $e_{k}$ and $r_{k}$ (error and residual)
MATH (Error and residual)
Note that
MATH (Error and residual 2)




A. Quadratic form minimum.
B. Method of steepest descent.
C. Method of conjugate directions.
D. Method of conjugate gradients.
E. Convergence analysis of conjugate gradient method.
F. Preconditioning.
G. Recursive calculation.
H. Parallel subspace preconditioner.

Notation. Index. Contents.


















Copyright 2007