The method of least squares is often used to determine the arbitrary constants in an empirical formula or approximating function. If such a function is not linear in its unknowns, approximate values must first be obtained. Typically they are obtained graphically or as the result of physical supposition or similar experiment. This paper describes a program written to find first approximations for certain oscilloscope traces by: (1) displaying the trace on a cathode-ray tube (CRT) and, (2) imposing upon it a computer generated curve which (3) employs parameters arbitrarily supplied by an operator in a quest for visual coincidence. While the technique proved successful in this application, a greater value may lie in its having indicated a mechanism for further automation. In its present form the method might best be utilized as a tool for studying the behavior of selected approximating functions.

he numerical solutions of difference equations corresponding to differential equations of elliptic type ~re usually obtained by solving a set of linear equations of very high order.If the equations ~md unknowns are properly ordered, all of the nonzero coefficients ~re found near the principal diagonM.The matrix c~n then be p~rtitioned to form a compound matri× which is of triple-diagonal form.One method of solving the linear equations is by relaxation, but this is inefficient when many sets of linear equations having the same matrix of coefficients are to be solved.Direct methods have been proposed for the inversion of triple-diagonM compound matrices.These methods have the common feature that they require inversions of submutrices, which nmst then necessarily be assumed to be nonsingular.Thus, these methods are therefore not applicable in the most general ease of the triple-diagonal compound matrix.This report develops the inverse of any nonsingular triple-diagonM compound matrix wi~h no auxiliary assumptions.The inverse is expressed in terms of the matrix and of the elementary compound operators of a Gram-Schmidt process operating on the rows of the matrix.The elements of the elementary compound operators are obtMned recursively, and the ~ctu~l Gram-Schmidt process is bypassed.NurnericM results of the application of the method to several very restricted systems of line'~r equ~tions h~ving integer coefficients and known integer solutions are included in this report.

article Free Access Share on An Iterative Procedure for the Calculation of the Eigenvalues and Eigenvectors of a Real Symmetric Matrix Author: Richard Elton von Holdt University of California Radiation Laboratory, Livermore, Calif. University of California Radiation Laboratory, Livermore, Calif.View Profile Authors Info & Claims Journal of the ACMVolume 3Issue 3pp 223–238https://doi.org/10.1145/320831.320842Published:01 July 1956Publication History 2citation419DownloadsMetricsTotal Citations2Total Downloads419Last 12 Months11Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF