# Top numerical analysis topics: All: Trending topics

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## Top numerical analysis topics: All

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 fourth-order 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 lower-triangular matrix 1744
19 Curve fitting 1688
20 Trapezoidal rule â second-order 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 *Expectation-maximization algorithm 1190
27 Row echelon form â matrix in which all entries below a nonzero entry are zero 1167
28 Truncation â rounding a floating-point number by discarding all digits after a certain digit 1165
29 Simulated annealing 1148
30 Multiplication algorithm â general discussion, simple methods 1140
31 Gauss-Kronrod rules 1018
32 Density functional theory 995
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 B-spline 817
41 Bilinear interpolation 763
42 Condition number 762
43 Particle swarm optimization 729
44 Bicubic interpolation 701
45 Linear approximation 680
46 Arbitrary-precision 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 / âx using details of the IEEE floating-point 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 Finite-difference time-domain method â a finite-difference 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
66 Vandermonde matrix 467
67 Radial basis function (RBF) â a function of the form Æ(x) = Ï(|xâx<sub>0</sub>|) 466
68 Climate model 458
69 Round-off error 433
70 **BFGS method â rank-two update of the Jacobian in which the matrix remains positive definite 429
71 *Smoothed-particle 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 second-order 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 *Non-linear least squares 346
84 Tabu search 342
85 Newton's method in optimization 339
86 Midpoint method â a second-order 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 shift-and-add 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 Navier-Stokes equations 286
101 Level set method 285
102 Runge's phenomenon 282
103 Linear multistep method â the other main class of methods for initial-value 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 positive-definite matrices 263
107 *Quasi-Newton method â uses an approximation of the Jacobian: 263
108 Arithmetic precision 262
109 Computational electromagnetics 259
110 Power iteration 251
111 *Successive over-relaxation (SOR) â a technique to accelerate the GaussâSeidel 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 first-order method, based on (piecewise) constant approximation 237
115 Hermite interpolation 232
116 Trilinear interpolation 229
117 QR algorithm 228
118 Well-posed 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 floating-point numbers guaranteed to have the unknown number between them 220
125 Discrete Laplace operator â finite-difference 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
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 second-order method with two stages, or a third-order 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 particle-particle 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 functional-analytic reformulation of the PDE necessary for some methods 146
172 *Karmarkar's algorithm 145
173 *Semi-implicit 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 Five-point stencil â two-dimensional 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 **L-BFGS method â truncated, matrix-free 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 second-order variant of Godunov's scheme 125
189 De Casteljau's algorithm 124
190 **Broyden's method â uses a rank-one 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