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Rank  Topic  Wikipedia views Oct 21 2010 

1  Floating point number  5842 
2  Significant figures  5511 
3  Least squares â the objective function is a sum of squares  5167 
4  Newton's method â based on linear approximation around the current iterate; quadratic convergence  4746 
5  Fast Fourier transform â a fast method for computing the discrete Fourier transform  4096 
6  Discrete Fourier transform â can be viewed as trigonometric interpolation at equidistant points  3256 
7  *Genetic algorithm, Genetic programming  2822 
8  Gaussian elimination  2592 
9  Lagrange multipliers  2546 
10  Maxima and minima  2458 
11  Linear interpolation  2158 
12  Computational fluid dynamics (CFD)  1990 
13  Simpson's rule â fourthorder method, based on (piecewise) quadratic approximation  1925 
14  Spline (mathematics) â the piecewise polynomials used as interpolants  1919 
15  Propagation of uncertainty  1819 
16  Wavelet  1759 
17  Finite difference â the discrete analogue of a differential operator  1754 
18  LU decomposition â write a matrix as a product of an upper and a lowertriangular matrix  1744 
19  Curve fitting  1688 
20  Trapezoidal rule â secondorder method, based on (piecewise) linear approximation  1670 
21  Euler method â the most basic method for solving an ODE  1576 
22  Simplex algorithm  1512 
23  Approximation  1446 
24  Cholesky decomposition â for solving a system with a positive definite matrix  1276 
25  Methods of computing square roots  1250 
26  *Expectationmaximization algorithm  1190 
27  Row echelon form â matrix in which all entries below a nonzero entry are zero  1167 
28  Truncation â rounding a floatingpoint number by discarding all digits after a certain digit  1165 
29  Simulated annealing  1148 
30  Multiplication algorithm â general discussion, simple methods  1140 
31  GaussKronrod rules  1018 
32  Density functional theory  995 
33  Gradient descent  982 
34  Bisection method â simple and robust; linear convergence  953 
35  Lagrange polynomial  934 
36  Approximation error  919 
37  Conjugate gradient method (CG) â assumes that the matrix is positive definite  911 
38  Secant method â based on linear interpolation at last two iterates  883 
39  Chebyshev polynomials  819 
40  Bspline  817 
41  Bilinear interpolation  763 
42  Condition number  762 
43  Particle swarm optimization  729 
44  Bicubic interpolation  701 
45  Linear approximation  680 
46  Arbitraryprecision arithmetic  635 
47  Iterative method  630 
48  Computational chemistry  607 
49  *Linear least squares  589 
50  Cubic Hermite spline  588 
51  Fast inverse square root â calculates 1 / âx using details of the IEEE floatingpoint system  583 
52  List of finite element software packages  581 
53  Horner scheme  575 
54  Celestial mechanics  571 
55  Evolutionary algorithm, Evolution strategy  565 
56  Gibbs phenomenon  534 
57  Jacobi method  523 
58  Discretization  521 
59  Fixed point iteration  521 
60  Finitedifference timedomain method â a finitedifference method for electrodynamics  519 
61  Tridiagonal matrix algorithm â simplified form of Gaussian elimination for tridiagonal matrices  516 
62  Numerical differentiation  510 
63  Markov decision process  489 
64  Monte Carlo integration â takes random samples of the integrand  483 
65  Quadratic programming  471 
66  Vandermonde matrix  467 
67  Radial basis function (RBF) â a function of the form Æ(x) = Ï(xâx<sub>0</sub>)  466 
68  Climate model  458 
69  Roundoff error  433 
70  **BFGS method â ranktwo update of the Jacobian in which the matrix remains positive definite  429 
71  *Smoothedparticle hydrodynamics  399 
72  Rate of convergence â the speed at which a convergent sequence approaches its limit  385 
73  Computational physics  383 
74  Karatsuba algorithm â the first algorithm which is faster than straightforward multiplication  382 
75  Convex optimization  376 
76  Verlet integration â a popular secondorder method  375 
77  Exponentiation by squaring  373 
78  Nearest neighbor search  367 
79  Direct stiffness method â a particular implementation of the finite element method, often used in structural analysis  367 
80  False position method â secant method with ideas from the bisection method  362 
81  Lanczos resampling â based on convolution with a sinc function  350 
82  Numerical stability  349 
83  *Nonlinear least squares  346 
84  Tabu search  342 
85  Newton's method in optimization  339 
86  Midpoint method â a secondorder method with two stages  339 
87  Curse of dimensionality  335 
88  Difference quotient  329 
89  Explicit and implicit methods â implicit methods need to solve an equation at every step  324 
90  Galerkin method â a finite element method in which the residual is orthogonal to the finite element space  323 
91  Numerical weather prediction  322 
92  CORDIC â shiftandadd algorithm using a table of arc tangents  317 
93  Quasiconvex function  317 
94  Goertzel algorithm  308 
95  Finite volume method â based on dividing the domain in many small domains; popular in computational fluid dynamics  303 
96  Boundary element method â based on transforming the PDE to an integral equation on the boundary of the domain  291 
97  Pivot element â entry in a matrix on which the algorithm concentrates  291 
98  Householder transformation  287 
99  *Golden section search  287 
100  Lattice Boltzmann methods â for the solution of the NavierStokes equations  286 
101  Level set method  285 
102  Runge's phenomenon  282 
103  Linear multistep method â the other main class of methods for initialvalue problems  280 
104  Stiff equation â roughly, an ODE for which the unstable methods needs a very short step size, but stable methods do not  269 
105  Newton polynomial  267 
106  Lanczos algorithm â Arnoldi, specialized for positivedefinite matrices  263 
107  *QuasiNewton method â uses an approximation of the Jacobian:  263 
108  Arithmetic precision  262 
109  Computational electromagnetics  259 
110  Power iteration  251 
111  *Successive overrelaxation (SOR) â a technique to accelerate the GaussâSeidel method  251 
112  Dual problem, Shadow price  245 
113  Finite element method in structural mechanics â a physical approach to finite element methods  245 
114  Rectangle method â firstorder method, based on (piecewise) constant approximation  237 
115  Hermite interpolation  232 
116  Trilinear interpolation  229 
117  QR algorithm  228 
118  Wellposed problem  226 
119  Abramowitz and Stegun â book containing formulas and tables of many special functions  225 
120  Computational complexity of mathematical operations  224 
121  Radial basis function network â neural network using radial basis functions as activation functions  223 
122  Multivariate interpolation â the function being interpolated depends on more than one variable  222 
123  Stochastic optimization  221 
124  Interval arithmetic â represent every number by two floatingpoint numbers guaranteed to have the unknown number between them  220 
125  Discrete Laplace operator â finitedifference approximation of the Laplace operator  218 
126  Generalized minimal residual method (GMRES) â based on the Arnoldi iteration  216 
127  Constraint (mathematics)  215 
128  Orders of approximation  213 
129  Inverse distance weighting  212 
130  Fitness function â (esp. in genetic algorithms) an approximation to the objective function that is easier to evaluate  211 
131  Discrete element method â a method in which the elements can move freely relative to each other  205 
132  *Stochastic gradient descent  204 
133  No free lunch in search and optimization  201 
134  Interior point method  196 
135  Generating trigonometric tables  196 
136  Bernstein polynomial â basis of polynomials useful for approximating a function  193 
137  Spectral method â based on the Fourier transformation  191 
138  Significance arithmetic  190 
139  Reduced cost â cost for increasing a variable by a small amount  190 
140  *Large eddy simulation  188 
141  Preconditioner  183 
142  *Newton fractal  178 
143  Heun's method â either a secondorder method with two stages, or a thirdorder method with three stages  177 
144  Slerp  176 
145  Harmony search â mimicks the improvisation process of musicians  176 
146  Butterfly diagram  176 
147  **Semidefinite programming  176 
148  *Differential evolution  174 
149  Shooting method  173 
150  Richardson extrapolation  173 
151  Fast multipole method â hierarchical method for evaluating particleparticle interactions  172 
152  Krylov subspace  170 
153  Integer square root  169 
154  Slack variable  168 
155  Subdivision surface â constructed by recursively subdividing a piecewise linear interpolant  167 
156  Brent's method â combines bisection method, secant method and inverse quadratic interpolation  164 
157  Multigrid method â uses a hierarchy of nested meshes to speed up the methods  164 
158  Meshfree methods â does not use a mesh, but uses a particle view of the field  164 
159  *Divided differences  162 
160  *Nonlinear conjugate gradient method â generalization for nonlinear optimization problems  162 
161  Thin plate spline â a specific polyharmonic spline: r<sup>2</sup> log r  159 
162  Least absolute deviations  159 
163  Upwind scheme  157 
164  Romberg's method â Richardson extrapolation applied to trapezium rule  156 
165  *Line search  156 
166  Truncation error â error committed by doing only a finite numbers of steps  155 
167  Residual (numerical analysis)  155 
168  nth root algorithm  151 
169  Partially observable Markov decision process  147 
170  *Evolutionary programming  146 
171  Weak formulation â a functionalanalytic reformulation of the PDE necessary for some methods  146 
172  *Karmarkar's algorithm  145 
173  *Semiimplicit Euler method â variant of Euler method which is symplectic when applied to separable Hamiltonians  144 
174  Leapfrog integration â another name for Verlet integration  140 
175  Fivepoint stencil â twodimensional stencil consisting of a point and its four immediate neighbours on a rectangular grid  139 
176  Discontinuous Galerkin method â a Galerkin method in which the approximate solution is not continuous  138 
177  Farkas' lemma  136 
178  Riemann solver â a solver for Riemann problems (a conservation law with piecewise constant data)  135 
179  Smoothing spline  135 
180  Stochastic programming  131 
181  Jacobi eigenvalue algorithm â select a small submatrix which can be diagonalized exactly, and repeat  131 
182  Arnoldi iteration â based on Krylov subspaces  131 
183  **LBFGS method â truncated, matrixfree variant of BFGS method suitable for large problems  130 
184  Kahan summation algorithm  129 
185  Memetic algorithm  129 
186  Levinson recursion â for Toeplitz matrices  129 
187  Modal analysis using FEM â solution of eigenvalue problems to find natural vibrations  125 
188  MUSCL scheme â secondorder variant of Godunov's scheme  125 
189  De Casteljau's algorithm  124 
190  **Broyden's method â uses a rankone update for the Jacobian  122 
191  Corner solution  122 
192  Symplectic integrator â a method for the solution of Hamilton's equations that preserves the symplectic structure  120 
193  Collocation method â discretizes a continuous equation by requiring it only to hold at certain points  120 
194  Von Neumann stability analysis â all Fourier components of the error should be stable  116 
195  Relative difference â the relative difference between x and y is x â y / max(x, y)  116 
196  *Overlapadd method  115 
197  Linear programming relaxation â ignoring the integrality constraints in a linear programming problem  115 
