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This system of linear equations can be formulated as a matrix equation, involving the matrix $A$ and the vectors $x$ and $b$, of which $x$ is the solution to be determined. Certain implicit Finite Difference Methods eventually lead to a system of linear equations.
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One of the key methods for solving the Black-Scholes Partial Differential Equation (PDE) model of options pricing is using Finite Difference Methods (FDM) to discretise the PDE and evaluate the solution numerically. In this article we will present a NumPy/SciPy listing, as well as a pure Python listing, for the LU Decomposition method, which is used in certain quantitative finance algorithms.
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