Graduate Texts in Mathematics bridge the gap between passive study and creative
understanding, offering graduate-level introductions to advanced topics in mathematics. The …

This book is devoted to the computation of the elementary functions. Here, we call
elementary functions the most commonly used mathematical functions: sin, cos, tan, sin− 1 …

Decomposing dynamical systems in terms of orthogonal expansions enables the modelling/
approximation of a system with a finite length expansion. By flexibly tuning the basis …

It is shown that monic orthogonal polynomials on the unit circle are the characteristic
polynomials of certain five-diagonal matrices depending on the Schur parameters. This …

The analysis of orthogonal polynomials associated with general weights was a major theme
in classical analysis in the twentieth century, and undoubtedly will continue to grow in …

Adaptive Fourier series—a variation of greedy algorithm Page 1 Adv Comput Math (2011)
34:279–293 DOI 10.1007/s10444-010-9153-4 Adaptive Fourier series—a variation of …

For large scale problems, an effective approach for solving the algebraic Lyapunov equation
consists of projecting the problem onto a significantly smaller space and then solving the …

We present a unified and self-contained treatment of rational Krylov methods for
approximating the product of a function of a linear operator with a vector. With the help of …

Generalized rational Krylov decompositions are matrix relations which, under certain
conditions, are associated with rational Krylov spaces. We study the algebraic properties of …

One‐dimensional adaptive Fourier decomposition, abbreviated as 1‐D AFD, or AFD, is an
adaptive representation of a physically realizable signal into a linear combination of …