![]() NumPy is significantly more efficient than writing an implementation in pure Python. ![]() We will make use of the NumPy library to speed up the calculation of the Jacobi method. the value of $x$, is given by the following iterative equation: ![]() $A$ is split into the sum of two separate matrices, $D$ and $R$, such that $A=D R$. We begin with the following matrix equation: The algorithm for the Jacobi method is relatively straightforward. The Jacobi method is one way of solving the resulting matrix equation that arises from the FDM. The Black-Scholes PDE can be formulated in such a way that it can be solved by a finite difference technique. Jacobi's method is used extensively in finite difference method (FDM) calculations, which are a key part of the quantitative finance landscape. ![]() The Jacobi method is a matrix iterative method used to solve the equation $Ax=b$ for a known square matrix $A$ of size $n\times n$ and known vector $b$ or length $n$. We've already looked at some other numerical linear algebra implementations in Python, including three separate matrix decomposition methods: LU Decomposition, Cholesky Decomposition and QR Decomposition. This article will discuss the Jacobi Method in Python. ![]()
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