Abstract: | Modifications are proposed for the methods of steepest descent and conjugate gradients for the solution of multiparameter inverse problems in heat conduction.Notation A, B, L
linear operators
- u
element of the solution space U
- f
exact initial data
- f
error in the initial data
-
value of the error in the initial data
- A–1
inverse operator
- u(k)( )
k-th derivative of the function u
-
i( )
polynomials of degree i–1
- A*, B*, L*
operators conjugate to the operators A, B, L
- J(g)
discrepancy functional
- J'g
gradient of the discrepancy functional
-
n
i
depth of descent with respect to the i-th component of the antigradient of the discrepancy in the n-th iteration
-
m
length of the observation interval
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 264–269, August, 1980. |