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High Performance Algorithms for Toeplitz and block Toeplitz matrices

- TOEPLITZ MATRICES, SRIKANTH THIRUMALAI, Srikanth Thirumalai, Kyle Gallivan, Paul Van Dooren
- 1996

Fast algorithms to factor Toeplitz matrices have existed since the beginning of this century. The two most notable algorithms to factor Toeplitz matrices are the Schur and the Levinson-Durbin. The former factors the Toeplitz matrix itself while the latter factors the inverse. In this thesis, we present several high performance variants of the classical… (More)

This paper presents a block Schur algorithm to obtain a factorization of a symmetric block Toeplitz matrix. It is inspired by the various block Schur algorithms that have appeared in the literature but which have not considered the innuence of performance tradeoos on implementation choices. We develop a version based on block hyperbolic Householder… (More)

- Srikanth Thirumalai, Narendra Ahuja
- IEEE Trans. Neural Networks
- 1996

Concerns the 3D interpretation of image sequences showing multiple objects in motion. Each object exhibits smooth motion except at certain time instants when a motion discontinuity may occur. The objects are assumed to contain point features which are detected as the images are acquired. Estimating feature trajectories in the first two frames amounts to… (More)

This paper gives a look-ahead Schur algorithm for nding the symmetric factorization of a Hermitian block Toeplitz matrix. The method is based on matrix operations and does not require any relations with orthogonal polynomials. The simplicity of the matrix based approach ought to shed new light on other issues such as parallelism and numerical stability.

The classical Schur algorithm computes the LDL T factorization of a symmetric Toeplitz matrix in O(n 2) operations, but requires that all the principal minors of the matrix be nonsingular. Look-ahead schemes have been proposed to deal with matrices that have exactly singular principal minors 9], 11]. Unfortunately, these algorithms cannot be extended to… (More)

The Schur algorithm can be generalized to obtain the QR factorization of block Toeplitz matrices due to the low displacement rank of the matrix T T T. This generalized Schur algorithm has been outlined in 1] for scalar Toeplitz matrices. This algorithm can be trivially extended to block Toeplitz matrices. For the sake of continuity, we rst outline the… (More)

In this paper we present two algorithms-one to compute the QR factorization of nearly rank-deecient Toeplitz and block Toeplitz matrices and the other to compute the solution of a severely ill-conditioned Toeplitz least-squares problem. The rst algorithm is based on adapting the generalized Schur algorithm to Cauchy-like matrices and has some rank-revealing… (More)

HIGHLIGHTS • Five years of intensive research experiences on data mining in the most prestigious data mining research group in North America. • Generated pioneer work in applying data mining and machine learning techniques on multi-relational databases. (Most existing techniques are only applicable to single tables.) • Worked on 10 projects in both academia… (More)