Computational Science

numerical analyst, developer of the so-called "backward" error analysis

specialized in mathematical biology and numerical analysis

specialized in numerical analysis

He received the Turing Award in 1989 for "his fundamental contributions to numerical analysis."

In 1999, Demmel was elected a member of the National Academy of Engineering for contributions to numerical linear algebra and scientific computing.

Computational Physics

RANDU is an obsolete method for generating random numbers used primarily in the 1960s and 1970s.

the Crank-Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations.

In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.

an eigenvalue algorithm used in numerical linear algebra

are a broad class of computational algorithms based on repeated random sampling

He also devised the Monte-Carlo method widely used in solving mathematical problems using statistical sampling.

primarily intended for numerical computations

Carl Runge worked on a procedure for the numerical solution of algebraic equations

It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies.

an iterative method named after Johan Frederik Steffensen for numerical root-finding

In mathematics, and more specifically in numerical analysis, Householder's methods are a class of root-finding algorithms

is the operation of finding the fitted matrix

In computational physics, the term advection scheme refers to a class of numerical discretization methods for solving hyperbolic partial differential equations.

It was designed to allow high numbers of particles in simulations of molecular dynamics

In numerical analysis, the Weierstrass method or Durand-Kerner method

In numerical analysis, Laguerre's method

In numerical linear algebra, the biconjugate gradient stabilized method

In numerical analysis, the Cash-Karp method

Jeff's research has been mainly focused on the solution of difference and differential equations, with an emphasis on mathematical software.

Graeffe's method or Dandelin-Lobachesky-Graeffe method is an algorithm for finding all of the roots of a polynomial.

Aitken's delta-squared process or Aitken extrapolation is a series acceleration method used for accelerating the rate of convergence of a sequence.

is a root-finding algorithm developed in 1967 for simultaneous approximation of all the roots of a univariate polynomial.

the SIMPLE algorithm is a widely used numerical procedure to solve the Navier-Stokes equations.

lower-upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix multiplication and matrix decomposition).

In numerical analysis, the Runge-Kutta methods (English: RUUNG-ə-KUUT-tah) are a family of explicit and implicit iterative methods, which include the Euler method, used in discretization for the approximate solutions of differential equations.

Nelder-Mead method (also downhill simplex method, amoeba method, or polytope method) is a numerical method used to find a local minimum or maximum of an objective function in a multidimensional space.

QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix.

conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite.

Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization).

Gauss-Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations.

Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation.

Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710-1761).

Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the best in the unifo

Bareiss algorithm, named after Erwin Bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that are performed are guaranteed to be exact (there is no remainder).

ellipsoid method is an iterative method for minimizing convex functions over convex sets.

In numerical analysis, the Newton-Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f.

In numerical optimization, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems.

In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in k variables.

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers.

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations.

In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative.

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.

In numerical linear algebra, the Cuthill-McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth.

In numerical analysis, the FTCS (forward time-centered space) method is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations.

In numerical analysis and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the solution of ordinary differential equations.

In numerical analysis, a multigrid method (MG method) is an algorithm for solving differential equations using a hierarchy of discretizations.

In numerical analysis, Gauss-Legendre quadrature is a form of Gaussian quadrature for approximating the definite integral of a function.

In mathematics, the Runge-Kutta-Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential equations.