Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
Printable PDF file
I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
1. Finite differences.
2. Gauss-Hermite Integration.
A. Gram-Schmidt orthogonalization.
B. Definition and existence of orthogonal polynomials.
C. Three-term recurrence relation for orthogonal polynomials.
D. Orthogonal polynomials and quadrature rules.
E. Extremal properties of orthogonal polynomials.
F. Chebyshev polynomials.
3. Asymptotic expansions.
4. Monte-Carlo.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Gram-Schmidt orthogonalization.


iven a set MATH (finite or infinite $m$ ) of linearly independent elements of a linear space and a scalar product MATH , the Gram-Schmidt orthogonalization procedure delivers a set MATH of MATH -orthogonal elements such that MATH

We start by setting MATH For $k=2,...,m$ we subtract from $u_{k}$ the projection on MATH : MATH





Notation. Index. Contents.


















Copyright 2007