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.
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.

Quadratic form minimum.


(Quadratic form minimum) Suppose the matrix MATH is symmetric and positive definite. We consider the problem

MATH The problem ( Quadratic form minimum ) always have a unique solution, see the proposition ( Unbounded existence result ). In addition, if MATH then

MATH (Connection between SLA and minimization)
Indeed, MATH In addition, we have MATH see the formula ( Error and residual ).

Notation. Index. Contents.

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