MATRICI GENERATE
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* Toate matricile generate sunt de tip "general": n x n

Data de intrare comuna:
n = ordinul matricii A

1. HILBERT
Formula:
    A(i,j) = 1. /(i +j -1)

Matricea (A = Hn):
	1	1/2		...	1/n
 	1/2	1/3		...	1/(n+1)
	....	...	...	...
	1/n 1/(n+1) ... 1/(2n-1)


2. LOTKIN (A = Ln)
Aceeasi cu Hilbert, dar prima linie cu 1.

Matricea (A = Ln):
	1	1		...	1
 	1/2	1/3		...	1/(n+1)
	....	...	...	...
	1/n 1/(n+1) ... 1/(2n-1)


3. COMPANION
n = gradul polinomului p(x) = x^n +a_(n-1)*x^(n-1) +... +a_2*x2 +a_1*x +a_0

Matricea (A = C):
	0	0	0	...		-a_0
	1	0	0	...		-a_1
	0	1	0	...		-a_2
	...	...		...		...
	0	0	0	...	0	-a_(n-2)
	0	0	0	...	1	-a_(n-1)
	

4. WILKINSON_5 (Wilkinson - ordin 5)
n = 5
Intrare: z (real)

Formula:
    A(i,j) = z*1.8144/(i +j +1)

Exemplul z =1.:
Matricea (A = W5):
    
	0.604800  0.453600  0.362880  0.302400  0.259200
	
	0.453600  0.362880  0.302400  0.259200  0.226800
    
	0.362880  0.302400  0.259200  0.226800  0.201600
    
	0.302400  0.259200  0.226800  0.201600  0.181440
    
	0.259200  0.226800  0.201600  0.181440  0.164945

Nota: matricea W5 este Hilbert scalata.


5. WILKINSON_20 (Wilkinson - ordin 20)
n = 20
Intrare: alfa

Generare:
alpha =1D-10

a = 0.

do i =1,n
a(i,i) =float(i)
if(i <=n-1) a(i,i+1) =float(n)
enddo

a(n,1) = alpha

Matricea (A = W20; elementele nescrise sunt 0):
	1	20	.	.	.	.	.
	.	2	20	.	.	.	.
	.	.	3	20	.	.	.
	.	.	.	.	.	.	.
	.	.	.	.	.	.	.
	.	.	.	.	.	19	20
	alfa	.	.	.	.	.	20



6. CAUCHY
Intrare: X(n), Y(n) = vectori care definesc A.

Formula:
    A(i,j) = 1./(X(i) +Y(j))

Exemplu:
n = 5
X = (1, 3, 5, 8, 7), Y = (2, 4, 6, 10, 9)

Matricea (A):
	1/3	 1/5  1/7  1/11 1/10
    
	1/5  1/7  1/9  1/13 1/12
    
	1/7  1/9  1/11 1/15 1/14
    
	1/10 1/12 1/14 1/18 1/17
    
	1/9  1/11 1/13 1/17 1/16
	
7. BANDA
Intrare:
nc =semi-latimea de banda (inclusiv elementul diagonal)
c = semi-banda dreapta ( c(1) = elementul diagonal)

Nota:
Matricea este simetrica, dar va fi declarata de tip "general" (n x n).

Exemplu:
Intrare:
nc = 3
semi-banda = 4 1 1

Matricea A
	4	1	1	0	0
	1	4   	1   	1   	0
	1	1   	4   	1   	1   
	0	1   	1   	4   	1   
	0	0	1   	1   	4   

 
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