So how does the applet work?
LU Decomposition is done using the Matrix Size input and the First Matrix input field.  First one must enter the size of the matrix in the size field.  The size is the number of rows or columns in a square matrix.  Then the elements of the matrix must be input into the first input field. The form of the input is the following:

                    row1 elements .... row2 elements..............rown elements

Nothing except the values of each element in a row should be entered and each element should be separated by a space from the previous element entered.  The total number of elements entered should be equal to the square of the size of the matrix.  Once the two fields are filled, the user simply presses the LU Button, the LU decomposition is output below the input fields.

"Fast" Polynomial Multiplication is performed using the two larger input fields.  In each field enter the coefficients from lowest order to highest order of one of the polynomials, separating each coefficient by a space.  Once the coefficients are entered into the two fields, the user should press the FFT Button to perform the multiplication.  The resultant polynomials coefficients in increasing order will be outputted.

Examples

        Matrix                                              Size Input                                  Field Input
        1      2                                                     2                                           1 2 3 4
        3      4

        1    2    3
        4    5    6                                                  3                                    1 2 3 4 5 6 7 8 9
        7    8    9

        1     3      4       7
       15   21    3.1    10                                      4            1 3 4 7 15 21 3.1 10 9 6.2 3.5 20.12 2 32 8 18
        9    6.2   3.5  20.12
        2     32     8     18

If you multiply the Matrix L by the Matrix U that is ouput from the applet, you should get the matrix you input into the applet.  An example of a matrix that will give an error because and alpha was encountered that
equals zero is a matrix of size 4 with entries of 1 through 16.

Fast Polynomial Multiplication examples:

To Multiply:             (1 + x)(1+x)                        Enter in field 1:    1 1        Enter in field 2:   1 1
The Resutlt:              1 2 1 = (1 + 2x + x^2)

                                (1+x)(1 + 2x + 5x^2)                                    1 1                                  1 2 5
                                1 3 7 5 = (1 + 3x + 7x^2 + 5x^3)

The applet will take any two simple polynomials.  Be creative and see what you can do.  One warning:  if you input anything but numbers into the fields, the applet will throw and exception.

Bonus: Unfortunate I did not have a successful way to display the Tridiagonalization of a Matrix using Householder matrices, but the function is implemented in java (partial bonus?)

Have fun!!!!!!

frazier@cs