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- George E. Collins, Alkiviadis G. Akritas
- SYMSACC
- 1976

Uspensky's 1948 book on the theory of equations presents an algorithm, based on Descartes' rule of signs, for isolating the real roots of a squarefree polynomial with real coefficients. Programmed in SAC-1 and applied to several classes of polynomials with integer coefficients, Uspensky's method proves to be a strong competitor of the recently discovered… (More)

Given an m×n matrix A, with m ≥ n, the four subspaces associated with it are shown in Fig. 1 (see [1]). Fig. 1. The row spaces and the nullspaces of A and A T ; a 1 through a n and h 1 through h m are abbreviations of the alignerframe and hangerframe vectors respectively (see [2]). The Fundamental Theorem of Linear Algebra tells us that N (A) is the… (More)

- Alkiviadis G. Akritas
- Computing
- 1980

- Alkiviadis G. Akritas, Gennadi I. Malaschonok
- Mathematics and Computers in Simulation
- 2004

Let A be an m × n matrix with m ≥ n. Then one form of the singular-value decomposition of A is A = U T ΣV, where U and V are orthogonal and Σ is square diagonal. That is, UU T = I rank(A) , V V T = I rank(A) , U is rank(A) × m, V is rank(A) × n and Σ = σ 1 0 · · · 0 0 0 σ 2 · · · 0 0. .. 0 0 · · · σ rank(A)−1 0 0 0 · · · 0 σ rank(A) … (More)

- Alkiviadis G. Akritas
- SYMSAC
- 1986

In this paper an attempt is made to correct the misconception of several authors [1] that there exists a method by Upensky (based on Vincent's theorem) for the isolation of the real roots of a polynomial equation with rational coefficients. Despite Uspensky's claim, in the preface of his book [2], that he invented this method, we show that what Upensky… (More)

This paper is a review of results on computational methods of linear algebra over commutative domains. Methods for the following problems are examined: solution of systems of linear equations, computation of determinants, computation of adjoint and inverse matrices, computation of the characteristic polynomial of a matrix.

In this paper we compare two real root isolation methods using Descartes' Rule of Signs: the Interval Bisection method, and the Continued Fractions method. We present some time-saving improvements to both methods. Comparing computation times we conclude that the Continued Fractions method works much faster save for the case of very many very large roots.

- Alkiviadis G. Akritas, Stylianos D. Danielopoulos
- Computing
- 1980

- Alkiviadis G. Akritas
- ACM SIGSAM Bulletin
- 1978

The purpose of this short note is to make known to our community some of the results of my Ph.D. Dissertation [1]. More details can also be found elsewhere [2], [3].