Numerical Methods - Assignments and Solutions

SyDe312 - Numerical Methods
Assignments and Solutions

Stephen Birkett

Research Piano Design Organology Physical Systems Animal Growth Modelling Environmental Systems Teaching Linear Algebra Numerical Methods Topics and Lectures Assignments Tests Computational Mathematics Musical Instruments Music Erard Pleyel Lipp Marcia Hadjimarkos \|homepage\|	Assigned problems are listed below for each unit. References are to Atkinson/Han 3rd Edition. The links to solutions will become active when they are available for downloading. Try doing the problems before looking at the solutions!
	UNIT 0 - NUMERICAL COMPUTATION
		2.1 1acd *2.2* 1bde 5bde 6adg 9 10 14 16 18 19. Find the IEEE 754 standard single precision floating point values representing the decimal numbers: 666.7523, 3.1415926535, -3.0E127, 3.0E-127 *1.1* 2bc 7 8 *1.2* 5 8 *1.3* 9 10 11 [resources: IEEE Standard 754 Floating Point Numbers IEEE 754 Floating Point chop.m expSeriesPlot.m fidiff.m]	SOLUTIONS 0
	UNIT I - LINEAR ALGEBRA
		6.1 4 5 6 *6.2* (7) 9 10 6.3 1 2 5 [explore these with limiting precision using GEdemo.m ] *6.5* 1 3 4 6.4 2a [hand calc and solve the system] 1 [hand calc - use strict partial pivoting] 2bc [use Matlab] 5 6 Suppl. Cholesky problems 8 [use Matlab] 9 10 [tridiag.m can be downloaded from the publisher's website] *6.6* 1b 3 4 5 6 14[resources: cholesky.m] *7.2* 1a 12 14 Suppl. SVD problems	SOLUTIONS 1a SOLUTIONS 1b SOLUTIONS SVD
	UNIT II - ROOT FINDING AND NON-LINEAR SYSTEMS
		*3.4* 3 4 7 *3.1* bisect.m brackPlot.m 1 4 7* 8* *3.2* newton.m 1 2 10* 11* *3.3* 1 5 6 [using both secant and regula falsi methods] *3.5* 1* 2* 8* *7.3* newtonSys.m 2 3 5. For polynomial problems marked * repeat using: (a) the companion matrix method [use eig in matlab to get the eigenvalues] and (b) Laguerre's method, utilizing polynomial deflation where interesting / appropriate / desirable, e.g. in 3.5-8 where there is a quadruple root.	SOLUTIONS 2a SOLUTIONS 2b
	UNIT III - CURVE FITTING AND INTERPOLATION
		*7.1* 1, 3 Extra curvefit problems *4.1* 2, 3, 6, 7, 12, 24, 25, 28 *4.3* 1, 3, 7, 14 [explore solutions of these problems using the matlab spline function and basic curve fitting in the graphic screen and compare to hand solutions] Extra illustrative examples	SOLUTIONS 3
	UNIT IV - NUMERICAL INTEGRATION AND DIFFERENTIATION
		*5.1* 2adef, 3adef, 4b, 5a, 6. *5.3* 1 2adef 4b 5a Extra quadrature problems *5.4* 1ac, 2ac, 3ac, 9ac, 13. Quassian quadrature m-files	SOLUTIONS 4a SOLUTIONS 4b
	UNIT V - DIFFERENTIAL EQUATIONS
		*8.2* 1abdg (also use midpoint method and RK-4; compare the ratios as described). *8.5* 10bd, 11bd, 12 bd odeEuler.m odeMidpt.m odeRK4.m Extra illustrative examples	SOLUTIONS 5
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