SIAM Journal on Scientific and Statistical Computing

We consider the computation of higher order fold or limit points of two parameter-dependent nonlinear problems. A direct method is proposed and an efficient implementation of the direct method is presented. Numerical results for the thermal ignition ...

A modification (MAP) of the algorithm (AP) of Alefeld and Platzöder (SIAM J. Numer. Anal., 20 (1983), pp. 210–219) for the solution of systems of nonlinear algebraic equations which is similar to the modification (MKM) of the Krawczyk-Moore algorithm (...

A simple method for the conversion of decimal numbers to irreducible rational fractions is formulated using a continued fraction expansion. A condition has been found such that the conversion may be performed in a single-valued way for any set of ...

Systems of linear algebraic equations must be solved at each integration step in all commonly used methods for the numerical solution of systems of stiff IVPs for ODES. Frequently, a substantial portion of the total computational-work and storage ...

An algorithm based on multiple shooting is given for the numerical solution of singularly perturbed boundary value problems for the system $y' = f(x,y)$ with possible boundary layers at the endpoints. The algorithm does not require any explicit a priori ...

Systolic architectures due to Brent, Luk and Van Loan are today the most promising method for computing the symmetric eigenvalue and singular value decompositions in real time. These systolic arrays, however, are only able to decompose matrices of a ...

A parallel method for computing the QR-decomposition of an $n \times n$ matrix is proposed. It requires $O(n^2 )$ processors and $O(n)$ units of time. The method can be extended to handle an $m \times n$ matrix $(m \geqq n)$. The requirements then ...

In this paper we consider the problem of predicting where fill-in occurs in the orthogonal decomposition of sparse matrices using Householder transformations. We show that a static data structure can be used throughout the numerical computation, and ...

Computing confidence intervals for functions $\phi (x) = w^T x$, where $Kx = y + e$ and e is a normally distributed error vector, is a standard problem in multivariate statistics. In this work, we develop an algorithm for solving this problem if ...

The work of Young in 1950, see Young [1950], [1971], showed that the Red/ Black ordering and the natural rowwise ordering of matrices with Property A, such as those arising from the 5-point discretization of Poisson's equation, lead to SOR iteration ...

In this paper, we address the stability of the Sherman–Morrison–Woodbury formula. Our main result states that if the original matrices, A and B, are well conditioned, then there exists matrices U and V such that the Sherman–Morrison–Woodbury formula is ...

An algorithm for producing a triangular mesh in a convex polygon is presented. It is used in a method for the finite element triangulation of a complex polygonal region of the plane in which the region is decomposed into convex polygons. The interior ...

PLTMGC is a program package for solving nonlinear elliptic systems that have explicit dependence on a scalar parameter. In addition to being able to compute solutions for fixed parameter values, it can be used to solve the linear eigenvalue problem, ...

An efficient least-squares method with finite elements is used to simulate the viscous flow with surface tension in a partially liquid-filled, horizontal, rotating cylinder. Mixed interpolations are used for the method: the free boundary is interpolated ...

A technique for numerically solving the two-dimensonal time harmonic equations of elastody-namics on exterior domains is presented. The method is based on the numerical reaization of the limiting amplitude principle and on the construction of a modified ...

When particle methods are used to simulate the high Mach number collision of gas clouds particle streaming may occur because the particles can penetrate the interface between the clouds. We show how this penetration can be prevented by using an ...

In an earlier paper, the pseudo-spectral method was advocated as a fast and efficient method for studying the time evolution of solutions of reaction-diffusion problems in certain cases. In this paper we extend the method to follow steady-state ...

Formulas are given for the spherical harmonic coefficients of bicubic splines. These formulas are useful for determining a spectral approximation to a discrete function which may be defined on a latitude-longitude grid or at arbitrarily scattered points ...

The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versions.Any FFT can thus be converted, by a few indexing ...

In many applications one encounters the problem of approximating surfaces from data given on a set of scattered points in a two-dimensional domain. The global interpolation methods with Duchon's “thin plate splines” and Hardy's multiquadrics are ...

Quasi-random search methods for the extreme values of multivariable functions suffer from the defect that they often require a very large number of function evaluations. We introduce and analyze the device of “localization of search” that speeds up ...

To discover and summarize regular periodic variation in a time series, $\{ y_i ,t_i \} $, we may consider approximating the observed $y_i $ with a general smooth periodic function of $t_i $:\[ y_i \approx f \left( {\omega t_i } \right) \]where $f( \...

Some existing representations for the cumulative distribution function of positive definite quadratic forms in normal random variables lead to inefficient computational algorithms. These inefficiencies are overcome with the derivation of some ...

Variation diminishing splines provide an effective tool for modeling active elements in circuit simulation. Using quadratic tensor product splines and maintaining uniform sampling at the boundary by linear extension of the data yields an algorithm that ...