Computer Science and Numerical Methods Flashcards

Gaussian elimination is a direct method for solving:

Answer: Systems of linear algebraic equations

Gaussian elimination reduces an augmented matrix [A|b] to upper triangular form through row operations, then back-substitutes to find the solution vector.

Using 8-bit two's complement representation, the range of signed integers is:

Answer: -128 to 127

With 8 bits in two's complement, the most negative value is -128 (10000000) and the most positive is 127 (01111111).

The central difference approximation for the second derivative f''(x) is:

Answer: [f(x+h) - 2f(x) + f(x-h)] / h²

The second-order central difference formula for f''(x) combines f at x+h, x, and x-h with coefficients 1, -2, 1 divided by h².

For the bisection method to guarantee finding a root on interval [a, b], which condition must hold?

Answer: f(a) · f(b) < 0 (the function changes sign over the interval)

By the Intermediate Value Theorem, if f is continuous and f(a) · f(b) < 0, then at least one root must exist between a and b.

In object-oriented programming, inheritance primarily allows:

Answer: A subclass to acquire the methods and attributes of a parent class

Inheritance creates an is-a relationship where the child class automatically gains all accessible members of the parent, enabling code reuse.

The condition number of a matrix is used to measure:

Answer: The sensitivity of the linear system solution to small perturbations in inputs

A high condition number indicates an ill-conditioned matrix where small errors in the input vector b can cause large errors in the solution x.

The IEEE 754 standard specifies:

Answer: Binary floating-point number representation and arithmetic rules

IEEE 754 defines how floating-point numbers (single, double, extended precision) are stored in binary and how arithmetic operations behave, including rounding and special values like NaN and infinity.