Scientific Computing
An introduction using Maple and MATLAB

Walter Gander, Martin J. Gander, Felix Kwok

Published by Springer Verlag

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Chapter 1. Why Study Scientific Computing?

Chapter 2. Finite Precision Arithmetic

Matlab:

Exp.m
ExpUnstable.m
KahanSummation.m
Pinaive.m
Pistabil.m
Sqrt.m
Varianz.m
VarianzStabil.m

Chapter 3. Linear Systems of Equations

Matlab:

BackSubstitution.m
BackSubstitutionSAXPY.m
Cholesky.m
Cramer.m
DetLaplace.m
EliminationBandMatrix.m
EliminationGivens.m
Elimination.m
Growfactor.m
LUbyRank1.m
StoreBandMatrix.m
ThomasGivens.m
Thomas.m

Chapter 4. Interpolation

Matlab:

AitkenExtrapolation.m
AitkenInterpolation.m
BarycentricCoefficients.m
BarycentricInterpolation.m
LagrangeInterpolation.m
myIFFT.m
NewtonCoefficients.m
NewtonInterpolation.m
OrthogonalInterpolation.m
OrthogonalPolynomialCoefficients.m
SplineInterpolation.m
SplineFunction.txt
SplineScheme.txt

Chapter 5. Nonlinear Equations

Matlab:

BaseB2Decimal.m
Bisection.m
Chaos.m
Decimal2BaseB.m
EpsilonAlgorithmLowStorage.m
EpsilonAlgorithm.m
Horner.m
NewtonCorrection.m
Newton.m
NewtonMaehly.m
NewtonRoots.m
NewtonTaylorRoots.m
Nickel.m
NumericalJacobian.m
PlotEllipse.m
Taylor.m

Chapter 6. Least Squares Problems

Matlab:

AddColumnQR.m
AddRowQR.m
AlgebraicEllipseFit.m
ClassicalGramSchmidt.m
ConstrainedLSQ.m
ConstrainedTLS.m
CovarianceBjoerck.m
Covariance.m
DirectSum.m
DrawEllipse.m
FastGivens.m
GivensQR.m
GivensQTy.m
GivensQy.m
GramSchmidt.m
HouseholderQR.m
HouseholderQTy.m
HouseholderQy.m
HouseholderQyTest.m
HyperPlaneFit.m
LinearlyConstrainedLSQ.m
ModifiedGramSchmidt2.m
ModifiedGramSchmidt.m
ModifiedGramSchmidtTwice.m
NewtonLSQ.m
NullSpaceMethod.m
Partition.m
PlotFunctions.m
PlotLine.m
PlotPoints.m
ProcrustesFit.m
RemoveColumnQR.m
RemoveRowQR.m
TLS.m
UpdateQR.m

Maple:

chem.txt
hilbert.txt

Chapter 7. Eigenvalue Problems

Matlab:

Bidiagonalize.m
DifferentialQDStepShifted.m
DirectSum.m
GeneralizedGivensRotation.m
GivensRotation.m
Hessenberg1.m
Hessenberg.m
ImplicitQR.m
Jacobi1.m
Jacobi2.m
Jacobi.m
OrthogonalLRStepShifted.m
OrthogonalQDStepShifted.m
ProgressiveQDStepShifted.m
QDLine.m
QDLineSymmetric.m
QRStep.m
SVDGolubReinsch.m
Swing.m
testdqd.m
Tridiagonalize.m

Maple:

Trafodqds.txt
Transformations.txt

Chapter 8. Differentiation

Matlab:

BilliardFunction.m
DeriveDeterminant.m
Determinant.m
Lambert.m
LambertN.m
LambertNP.m
LambertW2.m
LambertW2P.m
LambertW.m

Maple:

Brachystochrone.txt
FiniteDifferenceFormula.txt
f.txt
secondderivatives.txt

Chapter 9. Quadrature

Matlab:

GaussByGolubWelschBruteForce.m
GaussByGolubWelsch.m
GaussByNewtonMaehly.m
GivensRotation.m
LobattoAdaptive.m
Romberg.m
SimpsonAdaptive.m
SimpsonsRule.m
TrapezoidalRule.m

Maple:

ClosedNewtonCotesRule.txt
Gauss.txt
Lanczos.txt
MidpointOpenNewtonCotesRule.txt
OpenNewtonCotesRule.txt

Chapter 10. Numerical Ordinary Differential Equations

Matlab:

Arenstorf.m
DEQseries.m
Dog.m
ForwardEuler.m
Heun.m
HeunNegative.m
ode12.m
RK4.m
Runge.m
TaylorMethod.m

Maple:

AdamsBashforth.txt
AdamsMoulton.txt
BDF.txt
DelayExample.txt
ExplicitLMM2.txt
ExplicitLMM.txt
ImplicitLMM.txt
ImplicitRK.txt
OrderConditionsRK.txt
RK2.txt
RK.txt

Chapter 11. Iterative Methods for Linear Systems

Matlab:

Rho.m
Arnoldi.m
BiCGequivBiORES.m
BiCG.m
BiORES.m
CG.m
FOM.m
Lanczos.m
MPE.m
NonSymmetricLanczos.m
PCG.m
Saad.m
TEA1.m
TEAequivTEA1.m
TEA.m

Maple:

Jordanblock.txt

Chapter 12. Optimization

Matlab:

AdmissibleBasis.m
BruteForcePartition.m
GenerateProblem.m
Minimize.m
NelderMead.m
Newton.m
Simplex.m
SpectralPartition.m
SteepestDescent.m
TrustRegionLinear.m
TrustRegionQuadratic.m
   
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