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This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vectorfin a Hilbert spaceH, a linear operatorAacting onH, and a vectorginHsatisfyingAf=g, one is interested in approximatingfby finite linear combinations ofg,Ag,A2g,A3g, … The closed subspace generated by the latter vectors is called the Krylov subspace ofHgenerated bygandA. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.After giving a broad introduction to the subject, examples...

In 1492, Angelo Poliziano published his Lamia, a praelectio, or opening oration to a course he would teach that academic year on Aristotle's Prior Analytics at the Florentine university. Having heard murmurings that he was not philosopher enough to teach the Aristotelian text, Poliziano strikes back, offering in effect a fable-tinted history of philosophy. More than a repudiation of local gossip, the text represents a rethinking of the mission of philosophy. This volume offers the first English translation, an edition of the Latin text, and four studies that set this rich example of humanist...