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.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
A. Elementary definitions of wavelet analysis.
B. Haar functions.
C. Multiresolution analysis.
D. Orthonormal wavelet bases.
a. Auxiliary function of OST.
b. Scaling equation for wavelet.
c. Existence of orthonormal wavelet bases.
E. Discrete wavelet transform.
F. Construction of MRA from scaling filter or auxiliary function.
G. Consequences and conditions for vanishing moments of wavelets.
H. Existence of smooth compactly supported wavelets. Daubechies polynomials.
I. Semi-orthogonal wavelet bases.
J. Construction of (G)MRA and wavelets on an interval.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Auxiliary function of OST.


(Scaling equation 3) Let MATH be an MRA and $m_{0}$ is the auxiliary function (as in the definition ( Scaling filter and auxiliary function )). Then the function $m_{0}$ satisfies the relationship MATH


According to the proposition ( OST property 1 ), we have for MATH MATH We use the proposition ( Scaling equation ). MATH We separate even and odd $n$ -terms. MATH According to the definition of $m_{0}$ , see the proposition ( Scaling equation ), MATH . MATH MATH We use the proposition ( OST property 1 ) again. MATH

Notation. Index. Contents.

Copyright 2007