Gauss quadrature based finite temperature Lanczos method

نویسندگان

چکیده

The finite temperature Lanczos method (FTLM), which is an exact diagonalization intensively used in quantum many-body calculations, formulated the framework of orthogonal polynomials and Gauss quadrature. main idea to reduce static dynamic quantities into weighted summations related one- two-dimensional quadratures. Then lower order quadrature, generated from iteration, can be applied approximate initial summation. This fills conceptual gap between FTLM kernel polynomial method, makes it easy apply techniques calculation.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Rational Gauss Quadrature

The existence of (standard) Gauss quadrature rules with respect to a nonnegative measure dμ with support on the real axis easily can be shown with the aid of orthogonal polynomials with respect to this measure. Efficient algorithms for computing the nodes and weights of an n-point Gauss rule use the n × n symmetric tridiagonal matrix determined by the recursion coefficients for the first n orth...

متن کامل

A Gauss–Lobatto quadrature method for solving optimal control problems

This paper proposes a direct approach for solving optimal control problems. The time domain is divided into multiple subdomains, and a Lagrange interpolating polynomial using the Legendre–Gauss– Lobatto points is used to approximate the states and controls. The state equations are enforced at the Legendre–Gauss–Lobatto nodes in a nonlinear programming implementation by partial Gauss–Lobatto qua...

متن کامل

Calculation of Gauss Quadrature Rules

Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also presented for c...

متن کامل

Gauss-Hermite interval quadrature rule

The existence and uniqueness of the Gaussian interval quadrature formula with respect to the Hermite weight function on R is proved. Similar results have been recently obtained for the Jacobi weight on [−1, 1] and for the generalized Laguerre weight on [0,+∞). Numerical construction of the Gauss–Hermite interval quadrature rule is also investigated, and a suitable algorithm is proposed. A few n...

متن کامل

Generalized anti-Gauss quadrature rules

Abstract. Gauss quadrature is a popular approach to approximate the value of a desired integral determined by a measure with support on the real axis. Laurie proposed an (n+1)-point quadrature rule that gives an error of the same magnitude and of opposite sign as the associated n-point Gauss quadrature rule for all polynomials of degree up to 2n + 1. This rule is referred to as an anti-Gauss ru...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Chinese Physics B

سال: 2022

ISSN: ['2058-3834', '1674-1056']

DOI: https://doi.org/10.1088/1674-1056/ac5986