In this thesis, several techniques are proposed for complexity reduction of a switched-adaptive vector linear prediction coding scheme (known as SIVP) with vector quantization of the prediction residual. Coding is performed on Line Spectral Frequencies representation of the power spectrum envelope used for acoustic transfer function modeling in the source/filter model for speech production. Most frequently, coding by switched-adaptive prediction is performed using only two prediction matrices to achieve the best possible quality of reconstructed speech. In this work, the potential of utilizing larger number of switched matrices is investigated that enables reduction of complexity of vector quantization that follows prediction. By applying several techniques proposed in the thesis complexity of prediction is further reduced. In the first proposed technique, prediction complexity is reduced by decreasing the number of nonzero elements in prediction matrices. The criterion for obtaining optimal patterns of nonzero elements in partially zeroed matrices is given as well as the design procedure for calculating the optimal values of these elements. The prediction gain obtained with resulting sparse matrices is the highest for the chosen total number of predictor nonzero elements. The effect of the number and the fullness of switched matrices of the predictor on the resulting coding quality and complexity has been analyzed. Also, the technique based on linear transformation has been proposed for increasing the quality of coding with prediction matrices having fixed, diagonal structure. In the second proposed approach, the reduction of prediction complexity has been accomplished by substituting the optimal full search of the switched matrices during prediction with binary-tree search. Suitable predictor design procedure and coding scheme have been realized. Apart from exploring techniques resulting in lower complexity, two approaches for increasing the coding quality of SIVP method with higher number of prediction matrices have also been investigated. In that sense, the principle of multiple prediction candidates has been applied. According to that, quantization is performed on several smallest prediction residuals, called prediction candidates, and not only on the one having the minimal squared norm. The matrix used for prediction of the current input vector is then determined based on the corresponding candidate that results with minimal distortion measure after quantization. The obtained quality improvement is analyzed pertaining to the chosen number of prediction candidates and prediction matrices. Predictor design procedure based on minimization of the quantization error instead of prediction error energy has also been proposed. The last proposed method is a combination of the above mentioned predictor design procedure, prediction candidate principle and technique with sparse prediction matrices described first. The influence of different values of several design parameters has been investigated. It was shown that a group of coders obtained by this method result in best compromise between coder quality and complexity. It was also found out that by utilizing these coders, even higher coding quality can be obtained than in the case of classical SIVP method with two prediction matrices and it is accompanied by an adequate complexity reduction at the same time. Based on the great number of designed coders and detailed analysis of obtained results as part of this thesis, it is possible to choose a coder meeting the requirements for various types of speech coding applications.