Numerical Methods in Engineering with MATLAB, Jaan Kiusalaas. List of Computer Programs (by Chapter)
Chapter 2. Systems of linear algebraic equations
- 2.2 gauss.m Gauss elimination
- 2.3 LUdec.m LU decomposition---decomposition phase
- 2.3 LUsol.m Solution phase for above
- 2.3 choleski.m Choleski decomposition---decomposition phase
- 2.3 choleskiSol.m Solution phase for above
- 2.4 LUdec3.m LU decomposition of tridiagonal matrices
- 2.4 LUsol3.m Solution phase for above
- 2.4 LUdec5.m LU decomposition of pentadiagonal matrices
- 2.4 LUsol5.m Solution phase for above
- 2.5 swapRows.m Interchanges rows of a matrix or vector
- 2.5 gaussPiv.m Gauss elimination with row pivoting
- 2.5 LUdecPiv.m LU decomposition with row pivoting
- 2.5 LUsolPivl.m Solution phase for above
- 2.7 gaussSeidel.m Gauss-Seidel method with relaxation
- 2.7 conjGrad.m Conjugate gradient method
Chapter 3. Interpolation and curve fitting
- 3.2 newtonPoly.m Evaluates Newton's polynomial
- 3.2 newtonCoeff.m Computes coefficients of Newton's polynomial
- 3.2 neville.m Neville's method of polynomial interpolation
- 3.2 rational.m Rational function interpolation
- 3.3 splineCurv.m Computes curvatures of cubic spline at the knots
- 3.3 splineEval.m Evaluates cubic spline
- 3.4 polynFit.m Computes coefficients of best-fit polynomial
- 3.4 stdDev.m Computes standard deviation for above * Chapter 4. Roots of equations
- 4.2 rootsearch.m Searches for and brackets root of an equation
- 4.3 bisect.m Method of bisection
- 4.4 ridder.m Ridder's method
- 4.5 newtonRaphson.m Newton-Raphson method
- 4.6 newtonRaphson2.m Newton-Raphson method for systems of equations
- 4.7 evalPoly.m Evaluates a polynomial and its derivatives
- 4.7 polyRoots.m Laguerre's method for roots of polynomials
Chapter 6. Numerical integration
- 6.2 trapezoid.m Recursive trapezoidal rule
- 6.3 romberg.m Romberg integration
- 6.4 gaussNodes.m Nodes and weights for Gauss-Legendre quadrature
- 6.4 gaussQuad.m Gauss-Legendre quadrature
- 6.5 gaussQuad2.m Gauss-Legendre quadrature over a quadrilateral
- 6.5 triangleQuad.m Gauss-Legendre quadrature over a triangle
Chapter 7. Initial value problems
- 7.2 euler.m Euler's method for solution of initial value problems
- 7.2 printSol.m Prints solution of initial value problem in tabular form
- 7.3 runKut4.m 4th order Runge-Kutta method
- 7.5 runKut5.m Adaptive (5th order) Runge-Kutta method
- 7.6 midpoint.m Midpoint method with Richardson extrapolation
- 7.6 bulStoer.m Simplified Bulirsch-Stoer method
Chapter 8. Two-point boundary value problems
- 8.2 linInterp.m Linear interpolation
- 8.2 shoot2.m Shooting method example for 2nd order differential eqs.
- 8.2 shoot3.m Shooting method example for 3rd order linear diff. eqs.
- 8.2 shoot4.m Shooting method example for 4th order differential eqs.
- 8.2 shoot4nl.m Shooting method example for 4th order differential eqs.
- 8.3 fDiff6.m Finite difference example for 2nd order linear diff. eqs.
- 8.3 fDiff7.m Finite difference example for 2nd order differential. eqs.
- 8.4 fDiff8.m Finite difference example for 4th order linear diff. eqs.
Chapter 9. Symmetric matrix eigenvalue problems
- 9.2 jacobi.m Jacobi's method
- 9.2 sortEigen.m Sorts eigenvectors in ascending order of eigenvalues
- 9.2 swapCols.m Interchanges columns of a matrix
- 9.2 stdForm.m Transforms eigenvalue problem into standard form
- 9.3 invPower.m Inverse power method with eigenvalue shifting
- 9.3 invPower5.m As above for pentadiagonal matrices
- 9.4 householder.m Householder reduction to tridiagonal form
- 9.5 sturmSeq.m Computes Sturm sequence of tridiagonal matrices
- 9.5 count\_eVals.m Counts the number of eigenvalues smaller than $\lambda $
- 9.5 gerschgorin.m Computes global bounds on eigenvalues
- 9.5 eValBrackets.m Smallest eigenvalues of a tridiag. matrix
- 9.5 eigenvals3.m Finds m smallest eigenvalues of a tridiagonal matrix
- 9.5 invPower3.m Inverse power method for tridiagonal matrices
Chapter 10. Introduction to optimization
- 10.2 goldBracket.m Brackets the minimum of a function
- 10.2 goldSearch.m Golden section search for the minimum of a function
- 10.3 powell.m Powell's method of minimization
- 10.4 downhill.m Downhill simplex method of minimization