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An algorithm which finds rational function extrapolations of the form R_(i(i+1)...(i+m))=(P_mu(x))/(P_nu(x))=(p_0+p_1x+...+p_mux^mu)/(q_0+q_1x+...+q_nux^nu) and can be used ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

A number of spellings of "Chebyshev" (which is the spelling used exclusively in this work) are commonly found in the literature. These include Tchebicheff, Čebyšev, ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

Given a symmetric positive definite matrix A, the Cholesky decomposition is an upper triangular matrix U with strictly positive diagonal entries such that A=U^(T)U. Cholesky ...

A circular pattern obtained by superposing parallel equally spaced lines on a set of concentric circles of increasing radii, then coloring the regions in chessboard fashion. ...

The downward Clenshaw recurrence formula evaluates a sum of products of indexed coefficients by functions which obey a recurrence relation. If f(x)=sum_(k=0)^Nc_kF_k(x) (1) ...

The complexity of a process or algorithm is a measure of how difficult it is to perform. The study of the complexity of algorithms is known as complexity theory. In general, ...

A cork plug is a three-dimensional solid that can stopper a square, triangular, or circular hole. There is an infinite family of such shapes. The shape with smallest volume ...

Given two crossed ladders resting against two buildings, what is the distance between the buildings? Let the height at which they cross be h and the lengths of the ladders ...