Brezinski C. Continued Fractions and Pade Approximants 1990

Textbook in PDF format

Pade approximants and continued fractions are typical examples of old domains (since continued fractions can be traced back at least to Euclid's g.c.d. algorithm more that 2000 years ago) which are nou in full vitality. Thi is due to their numerous applications in number theory, cryptography, statistics, numerical analysis, special functions, digital filtering, signal processing, fractals. etc. This renewal of interes is also due to their intimate connections with other important topics such as orthogonal polynomials, rational approximation, Gaussian quadraturesm extrapolation and convergence acceleration methods, solution of differential equations and so on.
Since the subject is very rapidly developing, it seemed that a book gathering carefully selected papers presenting the last results would be of interest. This book comes from a special issue of the IMACS journal Applied Numerical Mathematics(vol.
4. numbers 2-4, June 1988) plus some new contributions specially written for it. All the papers contained in the book are original and important.
On the asymptotic behavior of continued fractions.
A matrix Euclidean algorithm and the matrix minimal Pade approximation problem.
General T-fraction expansions for ratios of hypergeometric functions.
Instability and modification of Thiele interpolating continued fractions.
A review of branched continued fraction theory for the construction of multivariable rational approximants.
The convergence of Pade-type approximats to holomorphic functions of several complex variables.
The ordinary and matrix continued fractions in the theoretical analysis of Hermitian and relaxation operators.
Limit periodic iteration.
Convergence acceleration of continued fractions of Poincare's type.
Meromorphic continuation of functions given by limit k-periodic continued fractions.
Continued fractions in numerical analysis.
Pade-type and Pade approximants in several variables.
Relation between Pade-type approximation and polynomial interpolation in several variables.
Convergence acceleration of limit k-periodic continued fractions.
Solution of the strong Hamburger moment problem by Laurent continued fractions.
Computation of continued fractions by square-root modification: Reflections and examples.
Author Index