lánchoz

Lánczos is a Hungarian surname. In English-language references the name is commonly rendered as Lanczos. It is associated with several scientists of Hungarian origin, most prominently Cornelius Lanczos, who developed the Lanczos algorithm in numerical linear algebra. The original Hungarian spelling of the surname, Lánczos, reflects the historical orthography and pronunciation in Hungary.

The Lanczos method is an algorithm for computing a few eigenvalues and corresponding eigenvectors of large, sparse symmetric (Hermitian) matrices. It constructs an orthonormal basis for a Krylov subspace generated by the matrix and an initial vector, and it projects the matrix onto this basis to produce a small tridiagonal matrix. The eigenpairs of the tridiagonal matrix approximate those of the original as iterations proceed. The method is efficient for large-scale problems because it uses sparse operations and avoids forming dense matrices. Practical implementations require reorthogonalization to counteract loss of orthogonality in finite precision; numerous variants exist, including Lanczos bidiagonalization for singular value decomposition and stabilized forms for improved numerical stability.

Beyond the algorithm, Lánczos remains a surname of Hungarian origin, usually transliterated as Lanczos in English. The spelling "lánchoz" appears to be a misspelling or variant not commonly used in standard references. No other widely recognized concept carries the exact spelling "lánchoz" in major fields.