Row Convergence of Algebraic Approximations

Algebraic Approximations

Convergence Fields of Row-finite and Row-infinite Toeplitz Transformations

During a recent conversation, R . P. Agnew suggested a determination of the validity of the proposition that row-infinite Toeplitz transformations are more powerful than row-finite transformations . Before this proposition is examined, it is necessary to assign a precise meaning to it. Corresponding to every sequence s a regular rowfinite Toeplitz transformation A can be constructed such that t...

Multigrid Convergence of Surface Approximations

This report deals with multigrid approximations of surfaces. Surface area and volume approximations are discussed for regular grids (3D objects), and surface reconstruction for irregular grids (terrain surfaces). Convergence analysis and approximation error calculations are emphasized. 1 CITR, Tamaki Campus, University Of Auckland, Auckland, New Zealand Multigrid convergence of surface approxim...

Accelerating Convergence of Trigonometric Approximations

Lanczos has recently developed a method for accelerating the convergence of trigonometric approximations for smooth, nonperiodic functions by modifying their boundary behavior. The method is reformulated here in terms of interpolation theory and is shown to be related to the theory of Lidstone interpolation. Extensions given include a new type of modifying function and the establishment of crit...

Spline Approximations of Real Algebraic Surfaces

We use a combination of both symbolic and numerical techniques to construct several degree bounded G0 and G1 continuous, piecewise spline approximations of real implicit algebraic surfaces for both computer graphics and geometric modeling. These approximations are based upon an adaptive triangulation (a G0 planar approximation) of the real components of the algebraic surface, and include both s...