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MuPAD / Symbolic Math Toolbox ( Sorgatz and Wehmeier, 1999) provides the symbolic computation capability. The proposed computational implementation, called SymNumOpt, unifies the symbolic-numeric computations into an integrated framework.
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Wicaksono, Wolfgang Marquardt, in Computer Aided Chemical Engineering, 2013 4 Computational Implementation Investigate the poly function, which finds the characteristic equation for a matrix, and the polyeig function, which solves a polynomial eigenvalue problem of a specified degree.ĭanan S. Investigate some of the other numerical integration functions, such as integral, integral2 for double integrals, and integral3 for triple integrals. In the Command Window, type “odeexamples” to see some ODE example codes. Investigate the Ordinary Differential Equation (ODE) solve functions, such as ode23 and ode45, which use the Runge-Kutta integration methods. Investigate the norm function to find a vector or matrix norm. Investigate the functions that return eigenvalues and eigenvectors, such as eig and eigs. Investigate the blkdiag function, which will create a block diagonal matrix. Investigate linear algebra functions, such as rank for the rank of a matrix, or null, which returns the null space of a matrix.
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Investigate the fzero function, which attempts to find a zero of a function near a specified x value. Investigate the fminsearch function, which finds local minima for a function. Investigate the interp1 function, which does a table look-up to interpolate or extrapolate. Investigate passing matrices to the set functions, using the ‘rows’ specifier. Investigate the use of ‘R2012a’ to see future changes to the set functions versus the use of ‘legacy’ to preserve the previous values. Investigate the index vectors returned by the set functions. Investigate the flag introduced in R2015a to omit NaN in functions such as max, min median, etc. Investigate the moving statistical functions introduced in R2016a movmean, movsum, etc. Investigate filtering data, for example using the filter function. Investigate the corrcoef function, which returns correlation coefficients. However, I'm not sure what you have against vpa as it is actually a much cleaner way to do this: b1 = vpa(a)*x or b1 = vpa(a*x).Ω 1 / ( s 2 + ω 1 2 ) ∓ ω 2 / ( s 2 + ω 2 2 ) If you want a more automatic way of converting floating point values to "exact" decimal representations with sym, you might try something like this: syms xĠ.000000000000000000000000010000000000000000384948697491918*x Matlab has probably chosen the other method as the default because the representation is not easily confused with floating-point. sym(0.1,'d') uses the floating-point value of 0.1 to length digits. However, care should be taken in how you do this, as the following example illustrates: syms xĪs you know, many floating-point decimal values are not exact. If you want to use decimal approximation/representation, then you'll need to directly specify that. As per the documentation for sym, the default conversion method for numeric values is rational approximation/representation, the 'r' flag.