Looking for a function to be written in Java that does not require other libraries to find the smallest eigenvalue that solves this matrix equation Ax = Lambda Mx. X is a eigenvector and Lambda is an eigenvalue. Matrix A is real, symmetric and square. Matrix M is symmetric but can have zeros or negative values on the diagonal. This prevents many standard means of solving equation because M is ill-conditioned.
The best solutions I have found, and are implemented in some commercial softwares, is the Lanczos method and also the Subspace iteration method. There is C and Fortran code online that is implemented in highly respected libraries such as LAPACK.
I don't need all the eigenvalues, nor do I need any eigenvectors. The smallest eigenvalue is required. The Subspace method is claimed to be the best and fastest for this type of work. Once you think you have it completed and tested it, I will provide a few examples to verify.
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HI. As a Java expert with strong math background, I know how to calculate eigen value, and I believe I can finish your project perfectly. Please let me know your detailed requirements. Thanks.