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The fixed point iteration x n+1 = cos x n with initial value x 1 = −1.. An attracting fixed point of a function f is a fixed point x fix of f with a neighborhood U of "close enough" points around x fix such that for any value of x in U, the fixed-point iteration sequence , (), (()), ((())), … is contained in U and converges to x fix.
It supports multiple tabs, VBA macro and PDF converting. [10] Lotus SmartSuite Lotus 123 – for MS Windows. In its MS-DOS (character cell) version, widely considered to be responsible for the explosion of popularity of spreadsheets during the 80s and early 90s. [citation needed] Microsoft Office Excel – for MS Windows and Apple Macintosh ...
In computer science, a computation is said to diverge if it does not terminate or terminates in an exceptional state. [1]: 377 Otherwise it is said to converge.In domains where computations are expected to be infinite, such as process calculi, a computation is said to diverge if it fails to be productive (i.e. to continue producing an action within a finite amount of time).
Sheets also has the ability to import several spreadsheet formats, including XLS (Microsoft Excel), Applix Spreadsheet, Quattro Pro, CSV, dBase, Gnumeric, SXC (OpenOffice.org XML), Kexi and TXT. It supports export of OpenDocument Spreadsheet, SXC, Tables document, CSV, HTML, Gnumeric, TeX and TXT.
A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).
Microsoft Graph supports many different types of charts, but its output is dated. Office 2003 was the last version to use Microsoft Graph for hosting charts inside Office applications as OLE objects. Office 2007 – specifically, Excel 2007 – includes a new integrated charting engine, and the charts are native to the applications. The new ...
In asymptotic analysis in general, one sequence () that converges to a limit is said to asymptotically converge to with a faster order of convergence than another sequence () that converges to in a shared metric space with distance metric | |, such as the real numbers or complex numbers with the ordinary absolute difference metrics, if
If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.