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Suitable as supplemental reading in courses in differential and integral calculus, numerical analysis, approximation theory and computer-aided geometric design. Relations of mathematical objects to each other are expressed by transformations. The repeated application of a transformation over and over again, i.e., its iteration leads to solution of equations, as in Newton's method for finding roots, or Picard's method for solving differential equations. This book studies a treasure trove of iterations, in number theory, analysis and geometry, and applied them to various problems, many of them taken from international and national Mathematical Olympiad competitions. Among topics treated are classical and not so classical inequalities, Sharkovskii's theorem, interpolation, Bernstein polynomials, BŽzier curves and surfaces, and splines. Most of the book requires only high school mathematics; the last part requires elementary calculus. This book would be an excellent supplement to courses in calculus, differential equations,, numerical analysis, approximation theory and computer-aided geometric design.

Iterative methods (Mathematics) --- Transformations (Mathematics) --- Algorithms --- Differential invariants --- Geometry, Differential --- Iteration (Mathematics) --- Numerical analysis --- Iterative methods (Mathematics). --- Transformations (Mathematics).

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The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.

The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems.

The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.

Lineaire vergelijkingen. --- Projectiemethoden (wiskunde) --- Equations, Simultaneous --- Iterative methods (Mathematics) --- Itération (Mathématiques) --- Numerical solutions. --- -Iterative methods (Mathematics) --- #TELE:SISTA --- 519.6 --- 681.3*G13 --- Iteration (Mathematics) --- Numerical analysis --- Simultaneous equations --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Equations, Simultaneous - Numerical solutions.