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...Thecomputationof eigenvalues and eigenvectors ofverylargesparsematrices by christopher conway paige b sc e dip n a london university institute of computer science thesis submitted for the degree doctor philosophy april dedication to fran coise acknowledgments author is very grateful his supervisor dr m j bernal thoughtful guidance encouragement he would also like thank friends at their help discussions in particular christine fair mary della valle mrs mccluskey excellence typing addendum chris ivo panayotov latexing original during order provide this much improved version corrected errors format some extra newpage commands have now been entered so that pages roughly correspond those abstract several methods are available computing large sparse matrices but as yet no outstandingly good algorithm generally known symmetric matrix case one most elegant algorithms theoretically method minimized iterations developed lanczos reduces tri diagonal form from which eigensystem can easily be found...