Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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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.

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