A breakdown-free Lanczos type algorithm for solving linear systems.
A novel parallel algorithm based on the Gram-Schmidt method for tridiagonal linear systems of equations.
A Numerical Procedure for Computing the Moore-Penrose Inverse.
A parallel projection method for linear algebraic systems
A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.
A robust and efficient parallel SVD solver based on restarted Lanczos bidiagonalization.
A simple recursive estimator with on-line orthogonalization of the input sequence
A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms
The Lanczos method for solving systems of linear equations is implemented by using some recurrence relationships between polynomials of a family of formal orthogonal polynomials or between those of two adjacent families of formal orthogonal polynomials. A division by zero can occur in these relations, thus producing a breakdown in the algorithm which has to be stopped. In this paper, three strategies to avoid this drawback are discussed: the MRZ and its variants, the normalized and unnormalized...
Algorithms 80-81. Calculation of projections
An algebraic construction of discrete wavelet transforms
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids
Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many...