Java inverse matrix calculation

Question

I\'m trying to calculate the inverse matrix in Java.

I\'m following the adjoint method (first calculation of the adjoint matrix, then transpose this matrix and fina

Answer 1

Your algorithm to compute a determinant is indeed exponential. The basic problem is that you are computing from the definition, and the straight definition leads to an exponential amount of subdeterminants to compute. You really need to transform the matrix first before computing either its determinant or its inverse. (I thought of explaining about dynamic programming, but this problem cannot be solved by dynamic programming as the number of subproblems is exponential too.)

LU decomposition, as recommended by others, is a good choice. If you are new to matrix calculation, you might also want to look at Gaussian elimination to compute determinants and inverses, as that might be a bit easier to comprehend at first.

And one thing to remember in matrix inversion is numerical stability, since you are dealing with floating point numbers. All the good algorithm include permutations of rows and/or columns to choose the suitable pivots, as they are called. At least in Gaussian elimination, you want to, at each step, to permute the columns so that the element largest in absolute value is chosen as the pivot, as this is the stablest choice.