This article will discuss the Jacobi Method in Python.ĭoes not provide consumer credit reports and is not a consumer credit reporting agency. 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. 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 $n$. Jacobi's method is used extensively in finite difference method (FDM) calculations, which are a key part of the quantitative finance landscape. The Black-Scholes PDE can be formulated in such a way that it can be solved by a finite difference technique. The Jacobi method is one way of solving the resulting matrix equation that arises from the FDM. The algorithm for the Jacobi method is relatively straightforward. We begin with the following matrix equation: 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 $A=D+R$.
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