A symmetric matrix is one where ai j = aji for all i and j. In other words, [A] = [A]T. Such systems occur commonly in both mathematical and engineering/science problem contexts. Special solution

Eigenvalues and Eigenvectors in MATLAB Set of linear algebraic equations of the general form [A]{x}={b} Such systems are called nonhomogeneous because of the presence of the vector {b} on the right-hand side of the

Iterative Methods for Non-Linear Systems Successive Substitution The following is a set of two simultaneous nonlinear equations with two unknowns: In contrast to linear systems which plot as straight lines, these equations plot as

LU Factorization with MATLAB LU Factorization [A]{x}={b}

Tridiagonal Systems in MATLAB Certain matrices have a particular structure that can be exploited to develop efficient solution schemes. For example, a banded matrix is a square matrix that has all elements equal to

Gauss Elimination Method in MATLAB Simple Gauss Elimination using Cramer’s Rule Cramer’s rule is solution technique that is best suited to small numbers of equations. Before describing this method, we will briefly review the

Optimization in MATLAB – Part II In the previous tutorial, we started discussion about Optimization and in particular we talked about Golden – Section Search method of One – Dimensional Optimization. Now moving further,

Optimization in MATLAB – Part I Optimization is the process of creating something that is as effective as possible. As engineers, we must continuously design devices and products that perform tasks in an efficient

Brent’s Method Brent’s method is a “hybrid” method that combines aspects of the bisection and secant methods with some additional features that make it completely robust and usually very efficient. Brent’s root-location method is