In Sections 9.2 through 9.14 we provide an introduction to some of the Symbolic Toolbox features but it is not our intention to provide details of all the features. This feature allows the user to perform certain computations to an unlimited precision. In addition, the study of the accuracy of computations can be enhanced using the Symbolic Toolbox variable-precision arithmetic feature. For example, a user can test a given numerical algorithm by solving a test problem symbolically, providing it has a solution in the closed form, and compare this exact solution with a numerical solution. The symbolic gradient vector of a given nonlinear function, which is required for the conjugate gradient method for minimizing a nonlinear function (see Chapter 8)Īn important feature of the Symbolic Toolbox is that it allows an extra dimension of experimentation. The Jacobian for a system of nonlinear simultaneous equations (see Chapter 3) 3.
The symbolic first derivative of a given single-variable nonlinear function, which is required by Newton's method for the solution of single-variable nonlinear equations (see Chapter 3) 2. Since we are using the Symbolic Toolbox in the field of numerical analysis we begin by giving some examples of the beneficial application of this toolbox.
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