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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.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
3. Finite element method.
4. Construction of approximation spaces.
A. Finite element.
B. Averaged Taylor polynomial.
C. Stable space splittings.
D. Frames.
E. Tensor product splitting.
F. Sparse tensor product. Cure for curse of dimensionality.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Tensor product splitting.


roposition

(Tensor product splitting) Let $H_{1}$ and $H_{2}$ be Hilbert spaces and MATH and MATH are stable splittings for $H_{1}$ and $H_{2}$ respectively with condition numbers $\kappa_{1}$ and $\kappa_{2}$ . Then MATH is a stable splitting of $H_{1}\otimes H_{2}$ with condition number MATH .

Proof

According to the section ( Stable space splittings ) it suffices to derive the Schwarz operator for the collection MATH and show that it is symmetric, positive and has strictly positive bounds. Such derivation is a straightforward exercise.





Notation. Index. Contents.


















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