NA_WorkSheet Introduction

      The NA_WorkSheet is an aggregation of numerical algorithms collected into a single
   Java application/applet. The worksheet has been designed to allow a simple user
   interface for accessing and executing each numerical method. Each numerical analysis
   algorithm will normally require some type of input. The input will normally come in the
   form of an input equation/data and parameters for controlling the execution of the
   algorithm. Output from each algorithm approximation is directly available as either a
   solution or combination solution and intermediate data. The NA_Worksheet also
   provides the capability to graph an input equation with the ability to both translate and
   scale the resultant plot.

      Upon running the NA_Worksheet application/applet the user will be presented with
   a standard 800x600 pixel frame that will conform to the host workstation's look and
   feel, theme. The frame can be resized to any desired dimension. The user's interface
   for the worksheet is divided into a quadripartite. In the upper left quadrant is the graph
   panel. Here plots can be viewed of the equation that is input for analysis. The upper
   right panel holds the main input, where various numerical methods can be selected and
   executed. The panel also provides a text box where the input equation for analysis can
   be entered. Two main buttons allow the user to either execute the selected approximation
   or graph the input equation. The lower left panel houses several tabbed panes that allows
   data output to be viewed, function evaluation, or controls for the graph panel to be
   accessed. The graph tab also includes the present grid scaling on the graph and coordinate
   information. The final panel in the lower right quadrant is particular to each selected numerical
   approximation. This panel provides the parameter selection and input for each chosen
   numerical method. A condensed list of the panels and there names follows:
  
   Graph Panel - Upper left quadrant.
   Main Input Panel - Upper right quadrant
   Output/Graph Control Panel - Lower left quadrant
   Approximation Method Panel - Lower right quadrant

      As an example to the general functionality of the NA_WorkSheet, input into the Main Input
   Panel Equation for Analysis text box, "10*sin(x/2) + 4". Any equation input into this text
   box must reflect a valid numerical expression. Multiplication and division being reflected
   with the characters "*", and "/" respectively. The valid variable assignment in this equation
   must be "x". A graph can now be generated of the Equation for Analysis by pressing the
   Graph Equation/Data button on the Main Input Panel. The Graph Panel will now display
   the resultant plot if there was not a problem with the input expression. If there is a problem
   the Output/Graph Control Panel Data pane tab will display the error. Various parameters
   associated with the generated plot in the Graph Panel can now be manipulated and
   displayed. Select the Graph tab in the Output/Graph Control Panel to view these options.
   The plot can be translated or zoomed in or out with the buttons in this panel. Also when
   the mouse pointer is within the Graph Panel the Present Coordinate position is displayed
   at the bottom of the Graph pane tab. At the bottom of this tab is also shown the present
   Grid Scale and the value of a Selected Coordinate position if the left mouse button is
   clicked on the graph somewhere. Another feature of the Graph Panel in the worksheet
   is the ability to control the colors used for the axis, background, grid, and plot. These
   are controlled through the Graph MenuBar selection at the top of the NA_WorkSheet.
        
      Almost all approximations presently in the NA_WorkSheet will work with the
   Equation for Analysis. So its important to have a valid and correct expression. Lets now
   execute one of the approximations. In the Main Input Panel, select the Numerical
   Analysis Type "Polynomial Roots", if it is not already selected, from the pull down menu.
   Select the "Bisection" approximation listed in the Main Input Panel. The approximation's
   input panel should now be displayed in the Approximation Method Panel, lower right
   quadrant. Several text boxes are listed, in the Approximation Method Panel, "Interval
   Endpoint A", "Interval Endpoint B", "Approximation Tolerance", and "Number of Iterations".
   There should also be a lone checkbox labeled "Intermediate Output Data". The Bisection
   Approximation is called a Polynomial Root finding numerical method. The approximation
   will try to determine the value of x in our equation, f(x) = 10*sin(x/2) + 4, where f(x) = 0.
   In order for this particular approximation to achieve this it needs some hints. The hints
   are the two endpoints, Interval EndPoint A and Interval EndPoint B. Preferably there
   should be only one point between these values of x where f(x) will evaluate to zero. The
   graph can help us out here to select the two endpoints. With the mouse pointer over the
   graph left click to find two "Selected Coordinate" points on either side of where the sine
   function crosses f(x) = y = 0. Two such indeterminate points should be 5 and 10. Enter
   these two numbers for the "Interval Endpoint A" and "Interval Endpoint B". Now also
   enter "0.000001" for the "Approximation Tolerance", and "25" for the "Number of
   Iterations" in the Bisection Method Approximation's input panel. The execution of the
   approximation can now be accomplished by pressing the "Execute Approximation" button
   in the Main Input Panel. Results for each approximation will be displayed in the Output/
   Graph Control Panel Data pane tab text area. In this case "Root = 7.106218" should
   be displayed. Any errors associated with the execution of an approximation will also
   be displayed in this same text area.

      The NA_WorkSheet provides a generic framework for executing various numerical
   analysis methods/approximations. Most of the approximations in the worksheet generally
   follow the sample process given in the previous paragraph. Some approximations do
   require some additional input or do not work with the Equation for Analysis. All the
   approximations if possible will provide additional data output besides the resulting solution
   if the "Intermediate Data" checkbox is selected in the approximation's Method Input
   Panel. Each approximation will also store resulting data so that comparisons can be made
   between similar numerical methods. In the Output/Graph Control Panel Data pane text area
   results can also be appended and output to the standard system I/O. Future planned
   features also might include a more formal formatted resultant data, data file export, and
   generic printing of the particular setup/data of the worksheet's executing approximation.