This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.

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This IMA Volume in Mathematics and its Applications RECENT ADVANCES IN ITERATIVE METHODS is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra. " Large systems of matrix equations arise frequently in applications and they have the prop erty that they are sparse and/or structured. The purpose of this workshop was to bring together researchers in numerical analysis and various ap plication areas to discuss where such problems arise and possible meth ods of solution. The last two days of the meeting were a celebration dedicated...

Dieses Buch stellt eine Weiterentwicklung seines Vorgangers "Wissenschaft liches Rechnen und Differentialgleichungen: Eine EinfUhrung in die Numerische Mathematik "(Golub und Ortega 1992]) dar. Ziel des vorliegenden Buches ist es, die grundlegenden Ideen des Vektor-und Parallelrechnens im Rahmen der Einfiihrung in die Grundlagen numerischer Verfahren darzustellen. Dies ist un serer Meinung nach sowohl fUr Studenten der Informatik als auch der Natur und Ingenieurwissenschaften von Interesse. Es ist klar, dafi das Hachstleistungs rechnen in den kommenden Jahren eine wachsende Bedeutung in den...