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Stability of the High Frequency Fast Multipole Method for Helmholtz’ Equation in Three Dimensions
Stability limits for the high frequency plane wave expansion, which approximates the free space Green’s function in Helmholtz’ equation, are...
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Weak sufficient convergence conditions and applications for newton methods
The famous Newton—Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution...
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A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations
This paper is devoted to the numerical analysis of some finite volume discretizations of Darcy’s equations. We propose two finite volume schemes on...
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Local Sampling for Regular Wavelet and Gabor Expansions
The local behavior of regular wavelet sampling expansions is quantified. The term “regular” refers to the decay properties of scaling functions φ of...
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The Information Loss Error and the Jitter Error for Regular Sampling Expansions
We give upper bounds for the Information Loss Error of regular sampling expansions. We estimate this error for a wide class of sampling formulas...
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A Gaussian smoothing algorithm to generate trend curves
A Gaussian smoothing algorithm obtained from a cascade of convolutions with a seven-point kernel is described. We prove that the change of local sums...
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Fast Verification of Solutions for Sparse Monotone Matrix Equations
This paper concerns the problem of verifying the accuracy of a numerical solution for linear systems with a coefficient matrix being sparse and...
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Structured Backward Error and Condition Number for Linear Systems of the Type A* Ax = b
We present a formulation for the structured condition number and for the structured backward error for the linear system A* Ax = b , when the...
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Discretized Newman-Shapiro Operators and Jackson’s Inequality on the Sphere
Applying a quadrature rule with positive weights to some integral operators introduced by Newman and Shapiro we obtain generalized hyperinterpolation...
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Eigenvalues of symmetrizable matrices
New perturbation theorems for matrices similar to Hermitian matrices are proved for a class of unitarily invariant norms called Q -norms. These...
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Perturbation analysis of the orthogonal procrustes problem
Given two arbitrary real matrices A and B of the same size, the orthogonal Procrustes problem is to find an orthogonal matrix M such that the Frobenius...
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A survey of truncation error analysis for Padé and continued fraction approximants
To compute the value of a function f ( z ) in the complex domain by means of a converging sequence of rational approximants { f n ( z )} of a continued...
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A posteriori error estimates for linear equations
This paper describes upper and lower p -norm error bounds for approximate solutions of the linear system of equations Ax=b . These bounds imply that the...
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Are the coefficients of a polynomial well-conditioned functions of its roots?
We show that the coefficients of a polynomial can be rather illconditioned functions of its given roots. In certain cases, however, the coefficients...
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On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization
Two methods are presented which efficiently solve tridiagonal systems on vector supercomputers and parallel computers with a moderate degree of...
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A lower bound for the number of function evaluations in an error estimate for numerical integration
A popular practical way to estimate the error in numerical integration is to use two cubature formulae. In this paper we give a lower bound for the...
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A convergence theorem for Newton-like methods in Banach spaces
A convergence theorem for Newton-like methods in Banach spaces is given, which improves results of Rheinboldt [27], Dennis [4], Miel [15, 16] and...