Advanced Programming Guide

214 • Chapter 5: Numerical Programming in Maple• lu: LU decomposition• ode45: solve ordinary differential equation• qr: QR orthogonal-triangular decomposition• size: compute size of matrix• square: determine whether matrix is square• transpose: matrix transpositionSome support and utility commands are provided. MATLAB convertsall Maple structures to its representation of hardware floating-point arraysbefore it performs any computations. The results are usually Arrays withdata type float[8] (that is, hardware float entries). For more information,refer to ?Array and ?Matrix.For more information on all these commands and the Matlab packagein general, refer to the online help for ?Matlab. To learn howto start the MATLAB application from your Maple session, refer to?Matlab[openlink].5.6 ConclusionWith numerical techniques, you can solve equations which are otherwiseunsolvable, investigate the properties of complicated solutions, andquickly obtain numerical estimates.Symbolic calculations give precise representations, but in some casescan be expensive to compute even with a tool as powerful as Maple. Atthe other extreme, hardware floating-point arithmetic allows you fast computationdirectly from Maple. This involves, however, limited accuracy.Software floating-point offers a balance. As well as sometimes being muchfaster than symbolic calculations, you also have the option to control theprecision of your calculations, thus exerting control over errors.Software floating-point calculations and representations mimic theIEEE 754 standard representation closely, except for the great advantageof arbitrary precision. The similarity with this popular standardallows you to readily apply accumulation of error and numerical analysisprinciples contained in numerous texts and papers.